A183238 - OEIS

%I #6 Mar 12 2015 23:34:00

%S 1,1,65,47386,194139713,3033434015626,141528428949437282,

%T 16650678223240391821765,4364875648285724481960633921,

%U 2319673879587334552914376906604146,2319673881714199597935597727665884813690

%N Sums of multinomial coefficients to the 6th power.

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

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

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

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

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

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

%K nonn

%O 0,3

%A _Paul D. Hanna_, Jan 04 2011