cp's OEIS Frontend

A182963 G.f.: A(x) = exp( Sum_{n>=1} A183235(n)*x^n/n ) where A183235 is the sums of the cubes of multinomial coefficients.

%I A182963 #6 Mar 30 2012 18:37:23
%S A182963 1,1,5,86,4052,400401,71827456,21068995258,9429303819612,
%T A182963 6105894632883407,5493030296624140330,6644655430011095138676,
%U A182963 10523095865317003368417750,21337870239129956669159151372
%N A182963 G.f.: A(x) = exp( Sum_{n>=1} A183235(n)*x^n/n ) where A183235 is the sums of the cubes of multinomial coefficients.
%C A182963 Conjectured to consist entirely of integers.
%F A182963 a(n) = (1/n)*Sum_{k=1..n} A183235(k)*a(n-k) for n>0 with a(0)=1.
%e A182963 G.f.: A(x) = 1 + x + 5*x^2 + 86*x^3 + 4052*x^4 + 400401*x^5 +...
%e A182963 log(A(x)) = x + 9*x^2/2 + 244*x^3/3 + 15833*x^4/4 + 1980126*x^5/5 + 428447592*x^6/6 + 146966837193*x^7/7 +...+ A183235(n)*x^n/n +...
%o A182963 (PARI) {a(n)=polcoeff(exp(intformal(1/x*(-1+serlaplace(serlaplace(serlaplace(1/prod(k=1, n+1, 1-x^k/k!^3+O(x^(n+2))))))))), n)}
%Y A182963 Cf. A183235, A183239, A183241.
%K A182963 nonn
%O A182963 0,3
%A A182963 _Paul D. Hanna_, Jan 04 2011