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A172434 G.f.: Sum_{n>=0} a(n)*x^n/n!^4 = [ Sum_{n>=0} x^n/n!^4 ]^3.

%I A172434 #16 Jul 17 2020 13:03:05
%S A172434 1,3,51,1785,67635,2973753,146591529,7735733883,430208938035,
%T A172434 24954576411225,1496639801457801,92241539987122683,
%U A172434 5816057121183700521,373854785336483200155,24431647104881328618315,1619654401178752389082785
%N A172434 G.f.: Sum_{n>=0} a(n)*x^n/n!^4 = [ Sum_{n>=0} x^n/n!^4 ]^3.
%H A172434 Seiichi Manyama, <a href="/A172434/b172434.txt">Table of n, a(n) for n = 0..500</a>
%F A172434 a(n) = Sum_{k=0..n} C(n,k)^4 * Sum_{j=0..k} C(k,j)^4 = Sum_{k=0..n} C(n,k)^4 * A005260(k).
%e A172434 G.f.: A(x) = 1 + 3*x + 51*x^2/2!^4 + 1785*x^3/3!^4 + 67635*x^4/4!^4 +...
%e A172434 A(x)^(1/3) = 1 + x + x^2/2!^4 + x^3/3!^4 + x^4/4!^4 +...
%o A172434 (PARI) {a(n)=if(n<0, 0, n!^4*polcoeff(sum(m=0, n, x^m/m!^4+x*O(x^n))^3, n))}
%o A172434 (PARI) {a(n)=sum(k=0, n, binomial(n, k)^4*sum(j=0, k, binomial(k, j)^4))}
%Y A172434 Cf. A002893, A005260, A141057, A180350, A336270.
%K A172434 nonn
%O A172434 0,2
%A A172434 _Paul D. Hanna_, Jan 20 2011