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A180350 G.f.: Sum_{n>=0} a(n)*x^n/n!^5 = [ Sum_{n>=0} x^n/n!^5 ]^3.

%I A180350 #17 Jul 17 2020 17:05:24
%S A180350 1,3,99,9237,775971,83118753,10657602909,1463886204147,
%T A180350 215566192274211,33677584957306713,5492032622227428849,
%U A180350 928229455634614797447,161727023896151286167901,28905146810167510775300463
%N A180350 G.f.: Sum_{n>=0} a(n)*x^n/n!^5 = [ Sum_{n>=0} x^n/n!^5 ]^3.
%H A180350 Seiichi Manyama, <a href="/A180350/b180350.txt">Table of n, a(n) for n = 0..424</a>
%F A180350 a(n) = Sum_{k=0..n} C(n,k)^5 * Sum_{j=0..k} C(k,j)^5 = Sum_{k=0..n} C(n,k)^5 * A005261(k).
%e A180350 G.f.: A(x) = 1 + 3*x + 99*x^2/2!^5 + 9237*x^3/3!^5 + 775971*x^4/4!^5 +...
%e A180350 A(x)^(1/3) = 1 + x + x^2/2!^5 + x^3/3!^5 + x^4/4!^5 +...
%o A180350 (PARI) {a(n)=if(n<0, 0, n!^5*polcoeff(sum(m=0, n, x^m/m!^5+x*O(x^n))^3, n))}
%o A180350 (PARI) {a(n)=sum(k=0, n, binomial(n, k)^5*sum(j=0, k, binomial(k, j)^5))}
%Y A180350 Cf. A002893, A005261, A141057, A172434, A336270.
%K A180350 nonn
%O A180350 0,2
%A A180350 _Paul D. Hanna_, Jan 20 2011