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Values of a certain hypergeometric function. Not known to be always integer-valued.
3

%I #11 Jul 05 2018 11:22:06

%S 5,29,230,2260,25921,334105,4717653,71677935,1156559775,19624027967,

%T 347486715005,6382806114599,121036793631550,2360217764672530,

%U 47174734548813698,963862614738695410,20085285577742751859,426043585490101967355,9183714902258875988330

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

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

%F 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

%t a[n_] := 5*HypergeometricPFQ[{-n, n/2 + 7/2, n/2 + 4}, {5, 3}, -4];

%t Table[a[n], {n, 0, 16}] (* _Jean-François Alcover_, Feb 19 2018 *)

%Y Cf. A087659-A087661.

%K nonn

%O 0,1

%A _Bill Gosper_, Sep 26 2003

%E More terms from _Vladeta Jovovic_, Sep 30 2003