A183237 Sums of multinomial coefficients to the 5th power.

1, 1, 33, 8020, 8220257, 25688403126, 199758931567152, 3357348771315829641, 110013706232123658318433, 6496199364012472451887572970, 649619955166586474874295658148158, 104621943411970982740307507415589286391

Offset: 0

Author

Paul D. Hanna, Jan 04 2011

Keywords

• nonn

Comments

Equals sums of the 5th power of terms in rows of the triangle of multinomial coefficients (A036038).

Examples

			G.f.: A(x) = 1 + x + 33*x^2/2!^5 + 8020*x^3/3!^5 + 8220257*x^4/4!^5 +...
A(x) = 1/((1-x)*(1-x^2/2!^5)*(1-x^3/3!^5)*(1-x^4/4!^5)*...).
		

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..120

Crossrefs

Cf. A036038, A005651, A183240, A183235, A183236, A183238.

Programs

PARI

{a(n)=n!^5*polcoeff(1/prod(k=1, n, 1-x^k/k!^5 +x*O(x^n)), n)}

Formula

G.f.: Sum_{n>=0} a(n)*x^n/n!^5 = Product_{n>=1} 1/(1 - x^n/n!^5).

a(n) ~ c * (n!)^5, where c = Product_{k>=2} 1/(1-1/(k!)^5) = 1.03239096052278897179685563337623849923796538921602982416328969955606263213989... . - Vaclav Kotesovec, Feb 19 2015