A185402 a(n) = C(2n,n) * (7^n/n!^2) * Product_{k=0..n-1} (7k+2)*(7k+5).

1, 140, 79380, 62563200, 57288340200, 57169180452384, 60324072262534080, 66193973824733314560, 74770747698820830356700, 86365239335124673905181200, 101541339191092781603799640464

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..320

Formula

Self-convolution of A185401:

A185401(n) = (7^n/n!^2) * Product_{k=0..n-1} (14k+2)*(14k+5).

a(n) ~ cos(3*Pi/14) * 2^(2*n) * 7^(3*n) / (Pi*n)^(3/2). - Vaclav Kotesovec, Oct 23 2020

Example

G.f.: A(x) = 1 + 140*x + 79380*x^2 + 62563200*x^3 +...
A(x)^(1/2) = 1 + 70*x + 37240*x^2 + 28674800*x^3 +...+ A185401(n)*x^n +...

Mathematica

Table[Binomial[2n, n] 7^n/(n!)^2 Product[(7k+2)(7k+5), {k, 0, n-1}], {n, 0, 10}] (* Harvey P. Dale, May 10 2012 *)

Prog

(PARI) {a(n)=(2*n)!/n!^2*(7^n/n!^2)*prod(k=0, n-1, (7*k+2)*(7*k+5))}

Crossrefs

Cf. A184896, A185401, A185404.

Sequence in context: A189552 A181238 A211420 * A216729 A350614 A058939

Adjacent sequences: A185399 A185400 A185401 * A185403 A185404 A185405

Keyword

nonn

Author

Paul D. Hanna, Jan 26 2011

Status

approved