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

1, 70, 37240, 28674800, 25943525300, 25700693903192, 26985728598351600, 29506966670254735200, 33241442139458850123750, 38316302306082901242642500, 44974142994787866162564060800

Offset: 0

Author

Paul D. Hanna, Jan 25 2011

Keywords

• nonn

Examples

			G.f.: A(x) = 1 + 70*x + 37240*x^2 + 28674800*x^3 +...
A(x)^2 = 1 + 140*x + 79380*x^2 + 62563200*x^3 +...+ A185402(n)*x^n +...
		

Links

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

Crossrefs

Cf. A184895, A185402, A185403.

Programs

Mathematica

Table[(7^n/(n!)^2)*Product[(14*k + 2)*(14*k + 5), {k, 0, n - 1}], {n, 0, 50}] (* G. C. Greubel, Jun 29 2017 *)

PARI

{a(n)=(7^n/n!^2)*prod(k=0,n-1,(14*k+2)*(14*k+5))}

Formula

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

a(n) ~ 2^(2*n) * 7^(3*n) / (Gamma(1/7) * Gamma(5/14) * n^(3/2)). - Vaclav Kotesovec, Nov 19 2023