A183238 Sums of multinomial coefficients to the 6th power.

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

Offset: 0

Author

Paul D. Hanna, Jan 04 2011

Keywords

• nonn

Comments

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

Examples

			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)*...).
		

Crossrefs

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

Programs

PARI

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

Formula

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