A272099 Triangle read by rows, T(n,k) = C(n+1,k+1)*F([k-n, k-n-1], [-n-1], -1), where F is the generalized hypergeometric function, for n>=0 and 0<=k<=n.

1, 4, 1, 12, 5, 1, 32, 18, 6, 1, 80, 56, 25, 7, 1, 192, 160, 88, 33, 8, 1, 448, 432, 280, 129, 42, 9, 1, 1024, 1120, 832, 450, 180, 52, 10, 1, 2304, 2816, 2352, 1452, 681, 242, 63, 11, 1, 5120, 6912, 6400, 4424, 2364, 985, 316, 75, 12, 1

Offset: 0

Author

Peter Luschny, Apr 25 2016

Keywords

• nonn
• tabl

Comments

This triangle results when the first column is removed from A210038. - Georg Fischer, Jul 26 2023

Examples

			Triangle starts:
1;
4,    1;
12,   5,    1;
32,   18,   6,   1;
80,   56,   25,  7,   1;
192,  160,  88,  33,  8,   1;
448,  432,  280, 129, 42,  9,  1;
1024, 1120, 832, 450, 180, 52, 10, 1;
		

Crossrefs

A258109 (row sums), A008466 (alternating row sums), A001787 (col. 0), A001793 (col. 1), A055585 (col. 2).

Cf. A210038.

Programs

Maple

T := (n,k) -> binomial(n+1,k+1)*hypergeom([k-n, k-n-1], [-n-1], -1):
seq(seq(simplify(T(n,k)),k=0..n),n=0..9);

Mathematica

T[n_, k_] := Binomial[n+1, k+1] HypergeometricPFQ[{k-n, k-n-1}, {-n-1}, -1];
Table[T[n, k], {n, 0, 9}, {k, 0, n}] // Flatten (* Jean-François Alcover, Jul 22 2019 *)