OFFSET
1,2
LINKS
Alois P. Heinz, Rows n = 1..141, flattened
Cedric Chauve, S. Dulucq and O. Guibert, Enumeration of some labeled trees, Proceedings of FPSAC/SFCA 2000 (Moscow), Springer, pp. 146-157.
Yen-Jen Cheng, Sen-Peng Eu, Tung-Shan Fu, and Jyun-Cheng Yao, On q-Counting of Noncrossing Chains and Parking Functions, arXiv:2312.07351 [math.CO], 2023.
A. M. Khidr and B. S. El-Desouky, A symmetric sum involving the Stirling numbers of the first kind, European J. Combin., 5 (1984), 51-54. See Table 1.
FORMULA
T(n,k) = Sum_{m=k+1..n} (-1)^(k+1)*binomial(m,k+1)*Stirling1(n+1,n+1-m)*n^(n-m) with 0 <= k < n.
EXAMPLE
Triangle begins:
1
2 2
6 15 6
24 104 104 24
120 770 1345 770 120
720 6264 16344 16344 6264 720
...
MAPLE
T:= (n, k)-> add((-1)^(k+1)*binomial(m, k+1)*
Stirling1(n+1, n+1-m)*n^(n-m), m=k+1..n):
seq(seq(T(n, k), k=0..n-1), n=1..9);
MATHEMATICA
A071208[n_, k_] := Sum[(-1)^(k+1)*Binomial[m, k+1]*StirlingS1[n+1, n+1-m]*n^(n-m), {m, k+1, n}];
Table[A071208[n, k], {n, 10}, {k, 0, n-1}] (* Paolo Xausa, Jun 28 2024 *)
CROSSREFS
KEYWORD
AUTHOR
Cedric Chauve (chauve(AT)lacim.uqam.ca), May 16 2002
EXTENSIONS
Offset 1 from Alois P. Heinz, Jun 26 2024
STATUS
approved