A183236 - OEIS

%I #12 Mar 14 2015 12:03:42

%S 1,1,17,1378,354065,221300626,286871431922,688780254549829,

%T 2821284379712638737,18510450092641988146882,

%U 185104666826030540618018642,2710117456989714966261367339909,56196998736058707145628074314226034

%N Sums of multinomial coefficients to the 4th power.

%C Equals sums of the 4th power of terms in rows of the triangle of multinomial coefficients (A036038).

%H Vaclav Kotesovec, <a href="/A183236/b183236.txt">Table of n, a(n) for n = 0..140</a>

%F G.f.: Sum_{n>=0} a(n)*x^n/n!^4 = Product_{n>=1} 1/(1 - x^n/n!^4).

%F a(n) ~ c * (n!)^4, where c = Product_{k>=2} 1/(1-1/(k!)^4) = 1.067493570155257423039762074691753715853526744464586468822554194836450214299287... . - _Vaclav Kotesovec_, Feb 19 2015

%e G.f.: A(x) = 1 + x + 17*x^2/2!^4 + 1378*x^3/3!^4 + 354065*x^4/4!^4 +...

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

%o (PARI) {a(n)=n!^4*polcoeff(1/prod(k=1, n, 1-x^k/k!^4 +x*O(x^n)), n)}

%Y Cf. A036038, A005651, A183240, A183235, A183237, A183238.

%K nonn

%O 0,3

%A _Paul D. Hanna_, Jan 04 2011