A087660 Values of a certain hypergeometric function. Not known to be always integer-valued.

4, 25, 228, 2620, 35164, 527663, 8613004, 150142594, 2759219428, 52953913663, 1053779339980, 21624992868276, 455655808661008, 9823903635742978, 216106936268122100, 4839230922051864504, 110093028451517403276, 2540412583358390378215, 59374626887737992823372

Offset: 0

Author

Bill Gosper, Sep 26 2003

Keywords

• nonn

Crossrefs

Cf. A087659-A087662.

Programs

Mathematica

a[n_] := 4*HypergeometricPFQ[{-n, (n + 5)/2, n/2 + 3}, {4, 2}, -4];
Table[a[n], {n, 0, 16}] (* Jean-François Alcover, Feb 19 2018 *)

Formula

a(n) = 4*hypergeom([ -n, n/2+5/2, n/2+3], [4, 2], -4).

Recurrence: (n+3)^2*(n+4)*(3*n - 2)*(3*n + 1)*a(n) = 10*(n+1)*(n+3)*(3*n - 2)*(3*n + 2)^2*a(n-1) - (n-1)*(n+1)*(3*n + 4)*(9*n^2 - 15*n + 14)*a(n-2) + (n-4)*(n-2)*(n-1)*(3*n + 1)*(3*n + 4)*a(n-3). - Vaclav Kotesovec, Jul 05 2018

Extensions

More terms from Vladeta Jovovic, Sep 30 2003