Displaying 1-10 of 28 results found.
a(n) = Sum_{k=0..n-1} binomial(n-1,k)*binomial(n+k,k). Also a(n) = T(n,n), array T as in A049600.
+20
21
0, 1, 4, 19, 96, 501, 2668, 14407, 78592, 432073, 2390004, 13286043, 74160672, 415382397, 2333445468, 13141557519, 74174404608, 419472490257, 2376287945572, 13482186743203, 76598310928096, 435730007006341, 2481447593848524, 14146164790774359
a(n) = T(n,2), array T as in A049600.
+20
20
0, 1, 4, 13, 38, 104, 272, 688, 1696, 4096, 9728, 22784, 52736, 120832, 274432, 618496, 1384448, 3080192, 6815744, 15007744, 32899072, 71827456, 156237824, 338690048, 731906048, 1577058304, 3388997632, 7264534528, 15535702016
a(n) = T(n,3), array T as in A049600.
+20
11
0, 1, 5, 19, 63, 192, 552, 1520, 4048, 10496, 26624, 66304, 162560, 393216, 940032, 2224128, 5214208, 12124160, 27983872, 64159744, 146210816, 331350016, 747110400, 1676673024, 3746562048, 8338276352, 18488492032
Triangle with columns built from row sums of the partial row sums triangles obtained from Pascal's triangle A007318. Essentially A049600 formatted differently.
+20
9
1, 1, 1, 1, 2, 1, 1, 4, 3, 1, 1, 8, 8, 4, 1, 1, 16, 20, 13, 5, 1, 1, 32, 48, 38, 19, 6, 1, 1, 64, 112, 104, 63, 26, 7, 1, 1, 128, 256, 272, 192, 96, 34, 8, 1, 1, 256, 576, 688, 552, 321, 138, 43, 9, 1, 1, 512, 1280, 1696, 1520, 1002, 501, 190, 53, 10, 1, 1, 1024, 2816, 4096
Number of loopless rooted planar maps with 3 faces and n vertices and no isthmuses. Also a(n)=T(4,n-3), array T as in A049600.
(Formerly M4490)
+20
4
1, 8, 20, 38, 63, 96, 138, 190, 253, 328, 416, 518, 635, 768, 918, 1086, 1273, 1480, 1708, 1958, 2231, 2528, 2850, 3198, 3573, 3976, 4408, 4870, 5363, 5888, 6446, 7038, 7665, 8328, 9028, 9766, 10543, 11360, 12218, 13118, 14061, 15048
a(n)=Sum{T(2i,n-2i): i=0,1,...,[ n/2 ]}, array T as in A049600.
+20
1
0, 0, 2, 3, 12, 25, 76, 182, 504, 1275, 3410, 8811, 23256, 60580, 159094, 415715, 1089648, 2850645, 7466468, 19541994, 51170460, 133951675, 350713222, 918141623, 2403786672, 6293097000, 16475700746, 43133687427, 112925875764
a(n)=T(n,n+2), array T as in A049600.
+20
1
0, 1, 6, 34, 190, 1059, 5908, 33028, 185076, 1039525, 5851626, 33006438, 186519138, 1055789511, 5985405000, 33979107336, 193143097288
a(n)=T(n,n+3), array T as in A049600.
+20
0
0, 1, 7, 43, 253, 1462, 8378, 47818, 272422, 1550927, 8829033, 50276013, 286430763, 1632808572, 9313861092, 53163187748, 303653552188
a(n) = (n+2)*2^(n-1).
(Formerly M2739 N1100)
+10
211
1, 3, 8, 20, 48, 112, 256, 576, 1280, 2816, 6144, 13312, 28672, 61440, 131072, 278528, 589824, 1245184, 2621440, 5505024, 11534336, 24117248, 50331648, 104857600, 218103808, 452984832, 939524096, 1946157056, 4026531840, 8321499136, 17179869184, 35433480192
Central Delannoy numbers: a(n) = Sum_{k=0..n} C(n,k)*C(n+k,k).
(Formerly M2942 N1184)
+10
190
1, 3, 13, 63, 321, 1683, 8989, 48639, 265729, 1462563, 8097453, 45046719, 251595969, 1409933619, 7923848253, 44642381823, 252055236609, 1425834724419, 8079317057869, 45849429914943, 260543813797441, 1482376214227923, 8443414161166173, 48141245001931263
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