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A183237 Sums of multinomial coefficients to the 5th power. 7
1, 1, 33, 8020, 8220257, 25688403126, 199758931567152, 3357348771315829641, 110013706232123658318433, 6496199364012472451887572970, 649619955166586474874295658148158, 104621943411970982740307507415589286391 (list; graph; refs; listen; history; text; internal format)
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

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Last modified November 13 12:45 EST 2019. Contains 329094 sequences. (Running on oeis4.)