|
%I #9 Jul 05 2018 12:27:14
%S 1,13,163,2353,40501,818821,18929023,489586273,13960500553,
%T 434386210141,14631135248731,529904353497553,20518350666873853,
%U 845225716194722773,36884609685305102071
%N a(n) = (6*n!/(n+5)) *binomial(n+5,n-1)* 6F6(-n+1, 1/5*n+1, 1/5*n+9/5, 1/5*n+8/5, 1/5*n+7/5, 1/5*n+6/5; 7/6, 4/3, 3/2, 5/3, 11/6, 2; -3125/46656), where 6F6(;;) is the generalized hypergeometric series.
%F a(n) = (7*n - 6)*a(n-1) - (n-1)*(21*n - 47)*a(n-2) + 35*(n-3)*(n-2)*(n-1)*a(n-3) - 35*(n-4)*(n-3)*(n-2)*(n-1)*a(n-4) + 21*(n-5)*(n-4)*(n-3)*(n-2)*(n-1)*a(n-5) - 7*(n-6)*(n-5)*(n-4)*(n-3)*(n-2)*(n-1)*a(n-6) + (n-7)*(n-6)*(n-5)*(n-4)*(n-3)*(n-2)*(n-1)*a(n-7). - _Vaclav Kotesovec_, Jul 05 2018
%t Table[6*n!/(n+5) * Binomial[n+5,n-1] * HypergeometricPFQ[{-n+1, 1/5*n+1, 1/5*n+9/5, 1/5*n+8/5, 1/5*n+7/5, 1/5*n+6/5}, {7/6, 4/3, 3/2, 5/3, 11/6, 2}, -3125/46656], {n,1,20}] (* _Vaclav Kotesovec_, Jul 05 2018 *)
%K nonn
%O 1,2
%A _Karol A. Penson_, Nov 21 2003
|
