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

1, 240, 205920, 243443200, 333578044800, 497645070354432, 784620394258821120, 1286100339771928412160, 2169691463830861104076800, 3742512413364745240724275200, 6570354792903146744615537541120

Offset

0,2

Links

Table of n, a(n) for n=0..10.

Formula

Self-convolution of A184887, where

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

a(n) ~ sqrt(sqrt(2)+2) * 2^(11*n - 1) / (Pi^(3/2) * n^(3/2)). - Vaclav Kotesovec, Oct 05 2020

Example

G.f.: A(x) = 1 + 240*x + 205920*x^2 + 243443200*x^3 +...
A(x)^(1/2) = 1 + 120*x + 95760*x^2 + 110230400*x^3 +...+ A184887(n)*x^n +...

Prog

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

Crossrefs

Cf. A184887, A184898.

Sequence in context: A035281 A008696 A047806 * A158792 A270051 A028678

Adjacent sequences: A184885 A184886 A184887 * A184889 A184890 A184891

Keyword

nonn

Author

Paul D. Hanna, Jan 25 2011

Status

approved