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A183238 Sums of multinomial coefficients to the 6th power. 7
1, 1, 65, 47386, 194139713, 3033434015626, 141528428949437282, 16650678223240391821765, 4364875648285724481960633921, 2319673879587334552914376906604146, 2319673881714199597935597727665884813690 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Equals sums of the 6th power of terms in rows of the triangle of multinomial coefficients (A036038).

LINKS

Table of n, a(n) for n=0..10.

FORMULA

G.f.: Sum_{n>=0} a(n)*x^n/n!^6 = Product_{n>=1} 1/(1 - x^n/n!^6).

EXAMPLE

G.f.: A(x) = 1 + x + 65*x^2/2!^6 + 47386*x^3/3!^6 + 194139713*x^4/4!^6 +...

A(x) = 1/((1-x)*(1-x^2/2!^6)*(1-x^3/3!^6)*(1-x^4/4!^6)*...).

PROG

(PARI) {a(n)=n!^6*polcoeff(1/prod(k=1, n, 1-x^k/k!^6 +x*O(x^n)), n)}

CROSSREFS

Cf. A036038, A005651, A183240, A183235, A183236, A183237.

Sequence in context: A278795 A289946 A219564 * A103345 A291456 A269794

Adjacent sequences:  A183235 A183236 A183237 * A183239 A183240 A183241

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Jan 04 2011

STATUS

approved

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Last modified July 12 15:09 EDT 2020. Contains 335665 sequences. (Running on oeis4.)