A184895 a(n) = (7^n/n!^2) * Product_{k=0..n-1} (14k+1)*(14k+6).

1, 42, 22050, 16909900, 15269639700, 15109613875944, 15853342647837688, 17325438750851187600, 19510609713302293636050, 22482485054570487449402900, 26382746561837375612125315092, 31419888802098260334367621118904

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) = A184896(n) where A184896(n) = C(2n,n) * (7^n/n!^2)*Product_{k=0..n-1} (7k+1)*(7k+6).

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

Example

G.f.: A(x) = 1 + 42*x + 22050*x^2 + 16909900*x^3 +...
A(x)^2 = 1 + 84*x + 45864*x^2 + 35672000*x^3 +...+ A184896(n)*x^n +...

Mathematica

FullSimplify[Table[2^(2*n) * 7^(3*n) * Gamma[n+1/14] * Gamma[n+3/7] / (Gamma[3/7] * Gamma[1/14] * Gamma[n+1]^2), {n, 0, 15}]] (* Vaclav Kotesovec, Jul 03 2014 *)

Prog

(PARI) {a(n)=(7^n/n!^2)*prod(k=0, n-1, (14*k+1)*(14*k+6))}

Crossrefs

Cf. A184896; variants: A184424, A178529, A184891, A092870, A184897.

Sequence in context: A095423 A174766 A265191 * A263058 A299503 A159433

Adjacent sequences: A184892 A184893 A184894 * A184896 A184897 A184898

Keyword

nonn

Author

Paul D. Hanna, Jan 25 2011

Status

approved