A180350 - OEIS

%I #17 Jul 17 2020 17:05:24

%S 1,3,99,9237,775971,83118753,10657602909,1463886204147,

%T 215566192274211,33677584957306713,5492032622227428849,

%U 928229455634614797447,161727023896151286167901,28905146810167510775300463

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

%H Seiichi Manyama, <a href="/A180350/b180350.txt">Table of n, a(n) for n = 0..424</a>

%F 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 G.f.: A(x) = 1 + 3*x + 99*x^2/2!^5 + 9237*x^3/3!^5 + 775971*x^4/4!^5 +...

%e A(x)^(1/3) = 1 + x + x^2/2!^5 + x^3/3!^5 + x^4/4!^5 +...

%o (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 (PARI) {a(n)=sum(k=0, n, binomial(n, k)^5*sum(j=0, k, binomial(k, j)^5))}

%Y Cf. A002893, A005261, A141057, A172434, A336270.

%K nonn

%O 0,2

%A _Paul D. Hanna_, Jan 20 2011