A177938 Triangle T(n,k) = (-1)^(k+n)*A054655(n,n-k), 0<=k<n, read by rows.

1, 1, 1, 6, 5, 1, 60, 47, 12, 1, 840, 638, 179, 22, 1, 15120, 11274, 3325, 485, 35, 1, 332640, 245004, 74524, 11985, 1075, 51, 1, 8648640, 6314664, 1961470, 336049, 34300, 2086, 70, 1, 259459200, 188204400, 59354028, 10630508, 1182769, 83720

Offset

0,4

Links

Table of n, a(n) for n=0..41.

Formula

Row generating function: Gamma(x+2n)/Gamma(x+n) = Sum_{k>=0) T(n,k)*x^k.

T(n, k) = n!*(-1)^k*[x^k] hypergeom([-n, -x + n - 1], [-n], 1). - Peter Luschny, Mar 22 2022

Example

[0]         1;
[1]         1,         1;
[2]         6,         5,        1;
[3]        60,        47,       12,        1;
[4]       840,       638,      179,       22,       1;
[5]     15120,     11274,     3325,      485,      35,     1;
[6]    332640,    245004,    74524,    11985,    1075,    51,    1;
[7]   8648640,   6314664,  1961470,   336049,   34300,  2086,   70,  1;
[8] 259459200, 188204400, 59354028, 10630508, 1182769, 83720, 3682, 92, 1;

Mathematica

p[x_, n_] = If[n == 0, 1, (n - 1)! / FunctionExpand[Beta[x + n, n]]];
Table[CoefficientList[p[x, n], x], {n, 0, 8}] // Flatten (* rewritten by Peter Luschny, Mar 22 2022 *)

Crossrefs

An unsigned, row-reversed variant of A054655.

Row sums are apparently A001813(n).

Cf. A001813, A054655.

Sequence in context: A238181 A197517 A102079 * A112282 A098866 A144689

Adjacent sequences: A177935 A177936 A177937 * A177939 A177940 A177941

Keyword

nonn,tabl

Author

Roger L. Bagula, May 15 2010

Status

approved