A258874 E.g.f.: exp( Sum_{n>=1} x^(4*n) / n^4 ) = Sum_{n>=0} a(n) * x^(4*n) / (4*n)!.

1, 24, 22680, 115684800, 1906520616000, 80659993905114624, 7746053047976698430976, 1560262733456599283808153600, 616206470499428864091871431168000, 445310234257659546728524999957770240000, 549601486893233034601458951894087488929628160

Offset

0,2

Comments

Sum_{n>=0} a(n)/(4*n)! = exp( Pi^4/90 ) = 2.95152868285335573659431343...

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..112

Example

E.g.f.: A(x) = 1 + 24*x^4/4! + 22680*x^8/8! + 115684800*x^12/12! + 1906520616000*x^16/16! +...
where
log(A(x)) = x^4 + x^8/2^4 + x^12/3^4 + x^16/4^4 + x^20/5^4 + x^24/6^4 +...
or,
log(A(x)) = 24*x^4/4! + 2520*x^8/8! + 5913600*x^12/12! + 81729648000*x^16/16! + 3892643213082624*x^20/20! +...

Mathematica

nmax=20; k=4; 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) = (4*n)!*polcoeff( exp(sum(m=1, n, (x^m/m)^4)+x*O(x^(4*n))), 4*n)}
for(n=0, 20, print1(a(n), ", "))

Crossrefs

Cf. A226837, A258873.

Sequence in context: A111404 A167066 A166338 * A188961 A153303 A272095

Adjacent sequences: A258871 A258872 A258873 * A258875 A258876 A258877

Keyword

nonn

Author

Paul D. Hanna, Jun 13 2015

Status

approved