OFFSET
0,5
COMMENTS
Triangle T(n,k), read by rows, given by [1, 0, 1, 0, 1, 0, 1, 0, 1, ...] DELTA [ -1, -2, -3, -4, -5, -6, -7, -8, ...], where DELTA is the operator defined in A084938. - Philippe Deléham, Aug 08 2005
LINKS
Michael De Vlieger, Table of n, a(n) for n = 0..11475 (rows n = 0..150, flattened)
Alnour Altoum, Hasan Arslan, and Mariam Zaarour, Cauchy numbers in type B, arXiv:2312.14652 [math.CO], 2023.
Ruedi Suter, Two analogues of a classical sequence, J. Integer Sequences, Vol. 3 (2000), #P00.1.8.
FORMULA
T(n,k) = A039757(n,n-k). - Petros Hadjicostas, Jul 12 2020
EXAMPLE
Triangle T(n,k) (with rows n >= 0 and columns k = 0..n) begins:
1;
1, -1;
1, -4, 3;
1, -9, 23, -15;
1, -16, 86, -176, 105;
1, -25, 230, -950, 1689, -945;
1, -36, 505, -3480, 12139, -19524, 10395;
... [Edited by Petros Hadjicostas, Jul 12 2020]
MATHEMATICA
a[n_, m_] := a[n, m] = a[n - 1, m - 1] - (2*n - 1)*a[n - 1, m]; a[n_, 0] := (-1)^n*(2*n - 1)!!; a[n_, n_] = 1; Table[a[n, m], {n, 0, 9}, {m, n, 0, -1}]] // Flatten (* Michael De Vlieger, Dec 29 2023, after Jean-François Alcover at A039757 *)
PROG
(PARI) row(n)=Vec(prod(i=1, n, 'x-2*i+1)) \\ Petros Hadjicostas, Jul 12 2020
CROSSREFS
KEYWORD
tabl,sign
AUTHOR
Ruedi Suter (suter(AT)math.ethz.ch)
EXTENSIONS
More terms from Petros Hadjicostas, Jul 12 2020
STATUS
approved