A184887 a(n) = (8^n/n!^2) * Product_{k=0..n-1} (16k+3)*(16k+5).

1, 120, 95760, 110230400, 148976385600, 220389705801216, 345522083206128640, 564061275098462085120, 948680557056225919411200, 1632480132897839426558156800, 2860496988068910156792264671232

Offset

0,2

Links

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

Formula

Self-convolution yields Sum_{k=0..n} a(n-k)*a(k) = A184888(n) where: A184888(n) = C(2n,n) * (8^n/n!^2)*Product_{k=0..n-1} (8k+3)*(8k+5).

Example

G.f.: A(x) = 1 + 120*x + 95760*x^2 + 110230400*x^3 +...
A(x)^2 = 1 + 240*x + 205920*x^2 + 243443200*x^3 +...+ A184888(n)*x^n +...

Mathematica

FullSimplify[Table[2^(11*n) * Gamma[n+3/16] * Gamma[n+5/16] / (Gamma[n+1]^2 * Gamma[3/16] * Gamma[5/16]), {n, 0, 15}]] (* Vaclav Kotesovec, Jul 03 2014 *)

Prog

(PARI) {a(n)=(8^n/n!^2)*prod(k=0, n-1, (16*k+3)*(16*k+5))}

Crossrefs

Cf. A184888, A184897.

Sequence in context: A058528 A001421 A107446 * A279579 A159735 A157879

Adjacent sequences: A184884 A184885 A184886 * A184888 A184889 A184890

Keyword

nonn

Author

Paul D. Hanna, Jan 25 2011

Status

approved