A184897 a(n) = (8^n/n!^2) * Product_{k=0..n-1} (16k+1)*(16k+7).

1, 56, 43792, 50098048, 67507119680, 99694514343424, 156121609461801984, 254663020429855285248, 428056704465033002591232, 736257531679856764456919040, 1289628692490437108622739390464

Offset: 0

Author

Paul D. Hanna, Jan 25 2011

Keywords

• nonn

Examples

			G.f.: A(x) = 1 + 56*x + 43792*x^2 + 50098048*x^3 +...
A(x)^2 = 1 + 112*x + 90720*x^2 + 105100800*x^3 +...+ A184898(n)*x^n +...
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..100

Crossrefs

Cf. A184898; variants: A184424, A178529, A184891, A092870, A184895.

Programs

Mathematica

FullSimplify[Table[2^(11*n) * Gamma[n+1/16] * Gamma[n+7/16] / (Gamma[n+1]^2 * Gamma[1/16] * Gamma[7/16]), {n, 0, 15}]] (* Vaclav Kotesovec, Jul 03 2014 *)

PARI

{a(n)=(8^n/n!^2)*prod(k=0,n-1,(16*k+1)*(16*k+7))}

Formula

Self-convolution yields Sum_{k=0..n} a(n-k)*a(k) = A184898(n) where A184898(n) = C(2n,n) * (8^n/n!^2)*Product_{k=0..n-1} (8k+1)*(8k+7).