A183238 Sums of multinomial coefficients to the 6th power.

1, 1, 65, 47386, 194139713, 3033434015626, 141528428949437282, 16650678223240391821765, 4364875648285724481960633921, 2319673879587334552914376906604146, 2319673881714199597935597727665884813690

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