A258873 E.g.f.: exp( Sum_{n>=1} x^(3*n) / n^3 ) = Sum_{n>=0} a(n) * x^(3*n) / (3*n)!.

1, 6, 450, 119280, 78863400, 109520755344, 286266696940224, 1296790704270547200, 9516008352506751089280, 106865158822383325849056000, 1750834760922461163750744303360, 40208636074137918720878142328872960, 1251936919292954052906797742408328704000

Offset

0,2

Comments

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

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..150

Example

E.g.f.: A(x) = 1 + 6*x^3/3! + 450*x^6/6! + 119280*x^9/9! + 78863400*x^12/12! +...
where
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 +...
or,
log(A(x)) = 6*x^3/3! + 90*x^6/6! + 13440*x^9/9! + 7484400*x^12/12! + 10461394944*x^15/15! +...

Mathematica

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 *)

Prog

(PARI) {a(n) = (3*n)!*polcoeff( exp(sum(m=1, n, (x^m/m)^3)+x*O(x^(3*n))), 3*n)}
for(n=0, 20, print1(a(n), ", "))

Crossrefs

Cf. A226837, A258874.

Sequence in context: A174777 A265168 A187514 * A244195 A338943 A232593

Adjacent sequences: A258870 A258871 A258872 * A258874 A258875 A258876

Keyword

nonn

Author

Paul D. Hanna, Jun 13 2015

Status

approved