A258873 - OEIS

%I #19 Jun 23 2015 20:58:56

%S 1,6,450,119280,78863400,109520755344,286266696940224,

%T 1296790704270547200,9516008352506751089280,

%U 106865158822383325849056000,1750834760922461163750744303360,40208636074137918720878142328872960,1251936919292954052906797742408328704000

%N E.g.f.: exp( Sum_{n>=1} x^(3*n) / n^3 )  =  Sum_{n>=0} a(n) * x^(3*n) / (3*n)!.

%C Sum_{n>=0} a(n)/(3*n)! = exp( zeta(3) ) = 3.3269531100024997901915178...

%H Vaclav Kotesovec, <a href="/A258873/b258873.txt">Table of n, a(n) for n = 0..150</a>

%e E.g.f.: A(x) = 1 + 6*x^3/3! + 450*x^6/6! + 119280*x^9/9! + 78863400*x^12/12! +...

%e where

%e log(A(x)) = x^3 + x^6/2^3 + x^9/3^3 + x^12/4^3 + x^15/5^3 + x^18/6^3 +...

%e or,

%e log(A(x)) = 6*x^3/3! + 90*x^6/6! + 13440*x^9/9! + 7484400*x^12/12! + 10461394944*x^15/15! +...

%t nmax=20; k=3; Table[(CoefficientList[Series[Exp[PolyLog[k,x^k]], {x,0,k*nmax}],x] * Range[0,k*nmax]!)[[k*n-k+1]], {n,1,nmax+1}] (* _Vaclav Kotesovec_, Jun 21 2015 *)

%o (PARI) {a(n) = (3*n)!*polcoeff( exp(sum(m=1, n, (x^m/m)^3)+x*O(x^(3*n))), 3*n)}

%o for(n=0, 20, print1(a(n), ", "))

%Y Cf. A226837, A258874.

%K nonn

%O 0,2

%A _Paul D. Hanna_, Jun 13 2015