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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. 0
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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..54.

EXAMPLE

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;

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-Fran├žois Alcover, Jul 22 2019 *)

CROSSREFS

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

Sequence in context: A232013 A246943 A106194 * A329033 A217234 A051290

Adjacent sequences:  A272096 A272097 A272098 * A272100 A272101 A272102

KEYWORD

nonn,tabl

AUTHOR

Peter Luschny, Apr 25 2016

STATUS

approved

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Last modified February 18 15:30 EST 2020. Contains 332019 sequences. (Running on oeis4.)