A183237 Sums of multinomial coefficients to the 5th power.

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

Offset

0,3

Comments

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

Links

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

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

Example

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)*...).

Prog

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

Crossrefs

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

Sequence in context: A316777 A057981 A219563 * A099828 A099827 A269793

Adjacent sequences: A183234 A183235 A183236 * A183238 A183239 A183240

Keyword

nonn

Author

Paul D. Hanna, Jan 04 2011

Status

approved