A294036 a(n) = 4^n*hypergeom([-n/4, (1-n)/4, (2-n)/4, (3-n)/4], [1, 1, 1], 1).

1, 4, 16, 64, 280, 1504, 9856, 70144, 498136, 3449440, 23506816, 160566784, 1115048896, 7905796864, 56994288640, 414928113664, 3034880623576, 22255957312864, 163667338903936, 1208070406612480, 8955840250934080, 66678657938510080

Offset

0,2

Comments

Diagonal of rational function 1/(1 - (x^4 + y^4 + z^4 + t^4 + 4*x*y*z*t)). - Gheorghe Coserea, Aug 04 2018

Links

Table of n, a(n) for n=0..21.

Formula

Let H(m, n, x) = m^n*hypergeom([(k-n)/m for k=0..m-1], [1 for k=0..m-2], x) then a(n) = H(4, n, 1).

a(n) ~ 2^(3*n + 2) / (Pi*n)^(3/2). - Vaclav Kotesovec, Nov 02 2017

Maple

T := (m, n, x) -> m^n*hypergeom([seq((k-n)/m, k=0..m-1)], [seq(1, k=0..m-2)], x):
lprint(seq(simplify(T(4, n, 1)), n=0..39));

Mathematica

Table[4^n * HypergeometricPFQ[{-n/4, (1-n)/4, (2-n)/4, (3-n)/4}, {1, 1, 1}, 1], {n, 0, 30}] (* Vaclav Kotesovec, Nov 02 2017 *)

Crossrefs

H(1, n, 1) = A000007(n), H(2, n, 1) = A000984(n), H(3, n, 1) = A006077(n), H(4, n, 1) = this seq., H(1, n, -1) = A000079(n), H(2, n, -1) = A098335(n), H(3, n, -1) = A294035(n), H(4, n, -1) = A294037(n).

Sequence in context: A142872 A113995 A212443 * A097679 A158778 A227313

Adjacent sequences: A294033 A294034 A294035 * A294037 A294038 A294039

Keyword

nonn

Author

Peter Luschny, Nov 02 2017

Status

approved