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A183237 Sums of multinomial coefficients to the 5th power.

%I A183237 #12 Mar 13 2015 22:53:52
%S A183237 1,1,33,8020,8220257,25688403126,199758931567152,3357348771315829641,
%T A183237 110013706232123658318433,6496199364012472451887572970,
%U A183237 649619955166586474874295658148158,104621943411970982740307507415589286391
%N A183237 Sums of multinomial coefficients to the 5th power.
%C A183237 Equals sums of the 5th power of terms in rows of the triangle of multinomial coefficients (A036038).
%H A183237 Vaclav Kotesovec, <a href="/A183237/b183237.txt">Table of n, a(n) for n = 0..120</a>
%F A183237 G.f.: Sum_{n>=0} a(n)*x^n/n!^5 = Product_{n>=1} 1/(1 - x^n/n!^5).
%F A183237 a(n) ~ c * (n!)^5, where c = Product_{k>=2} 1/(1-1/(k!)^5) = 1.03239096052278897179685563337623849923796538921602982416328969955606263213989... . - _Vaclav Kotesovec_, Feb 19 2015
%e A183237 G.f.: A(x) = 1 + x + 33*x^2/2!^5 + 8020*x^3/3!^5 + 8220257*x^4/4!^5 +...
%e A183237 A(x) = 1/((1-x)*(1-x^2/2!^5)*(1-x^3/3!^5)*(1-x^4/4!^5)*...).
%o A183237 (PARI) {a(n)=n!^5*polcoeff(1/prod(k=1, n, 1-x^k/k!^5 +x*O(x^n)), n)}
%Y A183237 Cf. A036038, A005651, A183240, A183235, A183236, A183238.
%K A183237 nonn
%O A183237 0,3
%A A183237 _Paul D. Hanna_, Jan 04 2011