A185403 a(n) = (7^n/n!^2) * Product_{k=0..n-1} (14k+3)*(14k+4).

1, 84, 44982, 34706112, 31430722680, 31154132320416, 32723954432339184, 35790656447712684672, 40328240610474258475572, 46491988990198595758628560, 54576945875594131561054066584

Offset

0,2

Links

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

Formula

Self-convolution yields Sum_{k=0..n} a(n-k)*a(k) = A185404(n) where A185404(n) = C(2n,n) * (7^n/n!^2)*Product_{k=0..n-1} (7k+3)*(7k+4).

a(n) ~ 2^(2*n) * 7^(3*n) / (Gamma(2/7) * Gamma(3/14) * n^(3/2)). - Vaclav Kotesovec, Nov 19 2023

Example

G.f.: A(x) = 1 + 84*x + 44982*x^2 + 34706112*x^3 +...
A(x)^2 = 1 + 168*x + 97020*x^2 + 76969200*x^3 +...+ A185404(n)*x^n +...

Mathematica

Table[(7^n/(n!)^2)*Product[(14*k + 3)*(14*k + 4), {k, 0, n - 1}], {n, 0, 50}] (* G. C. Greubel, Jun 29 2017 *)

Prog

(PARI) {a(n)=(7^n/n!^2)*prod(k=0, n-1, (14*k+3)*(14*k+4))}

Crossrefs

Cf. A184895, A185401, A185404.

Sequence in context: A275452 A269933 A184126 * A269897 A184896 A203093

Adjacent sequences: A185400 A185401 A185402 * A185404 A185405 A185406

Keyword

nonn

Author

Paul D. Hanna, Jan 26 2011

Status

approved