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A184897 a(n) = (8^n/n!^2) * Product_{k=0..n-1} (16k+1)*(16k+7). 6
1, 56, 43792, 50098048, 67507119680, 99694514343424, 156121609461801984, 254663020429855285248, 428056704465033002591232, 736257531679856764456919040, 1289628692490437108622739390464 (list; graph; refs; listen; history; text; internal format)
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) = A184898(n) where A184898(n) = C(2n,n) * (8^n/n!^2)*Product_{k=0..n-1} (8k+1)*(8k+7).

EXAMPLE

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 +...

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 *)

PROG

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

CROSSREFS

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

Sequence in context: A153472 A202579 A090218 * A159673 A009837 A308390

Adjacent sequences:  A184894 A184895 A184896 * A184898 A184899 A184900

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Jan 25 2011

STATUS

approved

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Last modified May 7 09:41 EDT 2021. Contains 343649 sequences. (Running on oeis4.)