A087661 Values of a certain hypergeometric function. Not known to be always integer-valued.

15, 99, 891, 9825, 125085, 1772775, 27303603, 449394792, 7809206685, 141975690765, 2681773580205, 52342675041564, 1051034305996356, 21635329605783960, 455225821135429270, 9766746945640199070, 213227240437260707169, 4728776305725359233781

Offset: 0

Author

Bill Gosper, Sep 26 2003

Keywords

• nonn

Crossrefs

Cf. A087659-A087662.

Programs

Mathematica

a[n_] := 15*HypergeometricPFQ[{-n, n/2 + 3, (n + 7)/2}, {5, 2}, -4];
Table[a[n], {n, 0, 15}] (* Jean-François Alcover, Feb 19 2018 *)

Formula

a(n) = 15*hypergeom([ -n, n/2+3, n/2+7/2], [5, 2], -4).

Recurrence: (n+4)^2*(n+5)*(3*n - 1)*(3*n + 1)*(3*n + 2)*a(n) = 6*(n+4)*(3*n - 1)*(45*n^4 + 180*n^3 + 264*n^2 + 151*n + 20)*a(n-1) - 3*(n-1)*(3*n + 5)*(9*n^4 + 9*n^3 - 2*n^2 + 68*n + 16)*a(n-2) + (n-5)*(n-2)*(n-1)*(3*n + 2)*(3*n + 4)*(3*n + 5)*a(n-3). - Vaclav Kotesovec, Jul 05 2018

Extensions

More terms from Vladeta Jovovic, Sep 30 2003