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

1, 3, 51, 1785, 67635, 2973753, 146591529, 7735733883, 430208938035, 24954576411225, 1496639801457801, 92241539987122683, 5816057121183700521, 373854785336483200155, 24431647104881328618315, 1619654401178752389082785

Offset: 0

Author

Paul D. Hanna, Jan 20 2011

Keywords

• nonn

Examples

			G.f.: A(x) = 1 + 3*x + 51*x^2/2!^4 + 1785*x^3/3!^4 + 67635*x^4/4!^4 +...
A(x)^(1/3) = 1 + x + x^2/2!^4 + x^3/3!^4 + x^4/4!^4 +...
		

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..500

Crossrefs

Cf. A002893, A005260, A141057, A180350, A336270.

Programs

PARI

{a(n)=if(n<0, 0, n!^4*polcoeff(sum(m=0, n, x^m/m!^4+x*O(x^n))^3, n))}

PARI

{a(n)=sum(k=0, n, binomial(n, k)^4*sum(j=0, k, binomial(k, j)^4))}

Formula

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).