cp's OEIS Frontend

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

%I A185401 #12 Nov 19 2023 07:24:08
%S A185401 1,70,37240,28674800,25943525300,25700693903192,26985728598351600,
%T A185401 29506966670254735200,33241442139458850123750,
%U A185401 38316302306082901242642500,44974142994787866162564060800
%N A185401 a(n) = (7^n/n!^2) * Product_{k=0..n-1} (14k+2)*(14k+5).
%H A185401 G. C. Greubel, <a href="/A185401/b185401.txt">Table of n, a(n) for n = 0..320</a>
%F A185401 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).
%F A185401 a(n) ~ 2^(2*n) * 7^(3*n) / (Gamma(1/7) * Gamma(5/14) * n^(3/2)). - _Vaclav Kotesovec_, Nov 19 2023
%e A185401 G.f.: A(x) = 1 + 70*x + 37240*x^2 + 28674800*x^3 +...
%e A185401 A(x)^2 = 1 + 140*x + 79380*x^2 + 62563200*x^3 +...+ A185402(n)*x^n +...
%t A185401 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 *)
%o A185401 (PARI) {a(n)=(7^n/n!^2)*prod(k=0,n-1,(14*k+2)*(14*k+5))}
%Y A185401 Cf. A184895, A185402, A185403.
%K A185401 nonn
%O A185401 0,2
%A A185401 _Paul D. Hanna_, Jan 25 2011