A087662 Values of a certain hypergeometric function. Not known to be always integer-valued.
5, 29, 230, 2260, 25921, 334105, 4717653, 71677935, 1156559775, 19624027967, 347486715005, 6382806114599, 121036793631550, 2360217764672530, 47174734548813698, 963862614738695410, 20085285577742751859, 426043585490101967355, 9183714902258875988330
Offset: 0
Keywords
Programs
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Mathematica
a[n_] := 5*HypergeometricPFQ[{-n, n/2 + 7/2, n/2 + 4}, {5, 3}, -4]; Table[a[n], {n, 0, 16}] (* Jean-François Alcover, Feb 19 2018 *)
Formula
a(n) = 5*hypergeom([ -n, n/2+7/2, n/2+4], [5, 3], -4).
Recurrence: (n+4)*(n+5)*(n+6)*(3*n + 2)*a(n) = 5*(n+5)*(3*n + 4)*(6*n^2 + 14*n + 9)*a(n-1) - (n-1)*(9*n^3 + 24*n^2 + 17*n - 20)*a(n-2) + (n-4)*(n-2)*(n-1)*(3*n + 5)*a(n-3). - Vaclav Kotesovec, Jul 05 2018
Extensions
More terms from Vladeta Jovovic, Sep 30 2003