A090134 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.

1, 13, 163, 2353, 40501, 818821, 18929023, 489586273, 13960500553, 434386210141, 14631135248731, 529904353497553, 20518350666873853, 845225716194722773, 36884609685305102071

Offset

1,2

Links

Table of n, a(n) for n=1..15.

Formula

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

Mathematica

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 *)

Crossrefs

Sequence in context: A250417 A212785 A133180 * A087400 A012828 A119539

Adjacent sequences: A090131 A090132 A090133 * A090135 A090136 A090137

Keyword

nonn

Author

Karol A. Penson, Nov 21 2003

Status

approved