A183236 Sums of multinomial coefficients to the 4th power.

1, 1, 17, 1378, 354065, 221300626, 286871431922, 688780254549829, 2821284379712638737, 18510450092641988146882, 185104666826030540618018642, 2710117456989714966261367339909, 56196998736058707145628074314226034

Offset: 0

Author

Paul D. Hanna, Jan 04 2011

Keywords

• nonn

Comments

Equals sums of the 4th power of terms in rows of the triangle of multinomial coefficients (A036038).

Examples

			G.f.: A(x) = 1 + x + 17*x^2/2!^4 + 1378*x^3/3!^4 + 354065*x^4/4!^4 +...
A(x) = 1/((1-x)*(1-x^2/2!^4)*(1-x^3/3!^4)*(1-x^4/4!^4)*...).
		

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..140

Crossrefs

Cf. A036038, A005651, A183240, A183235, A183237, A183238.

Programs

PARI

{a(n)=n!^4*polcoeff(1/prod(k=1, n, 1-x^k/k!^4 +x*O(x^n)), n)}

Formula

G.f.: Sum_{n>=0} a(n)*x^n/n!^4 = Product_{n>=1} 1/(1 - x^n/n!^4).

a(n) ~ c * (n!)^4, where c = Product_{k>=2} 1/(1-1/(k!)^4) = 1.067493570155257423039762074691753715853526744464586468822554194836450214299287... . - Vaclav Kotesovec, Feb 19 2015