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A185403
a(n) = (7^n/n!^2) * Product_{k=0..n-1} (14k+3)*(14k+4).
3
1, 84, 44982, 34706112, 31430722680, 31154132320416, 32723954432339184, 35790656447712684672, 40328240610474258475572, 46491988990198595758628560, 54576945875594131561054066584
OFFSET
0,2
LINKS
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
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Jan 26 2011
STATUS
approved