A226837 E.g.f.: exp( Sum_{n>=1} x^(2*n) / n^2 ) = Sum_{n>=0} a(n)*x^(2*n)/(2*n)!.

1, 2, 18, 380, 14980, 969192, 94438344, 13027041456, 2427908305680, 589565047637280, 181202801029384992, 68849741925654266304, 31716559209036029729856, 17426989484519712174940800, 11263849940254797456755356800, 8462659472067485322490892440320

Offset

0,2

Comments

Sum_{n>=0} a(n)/(2*n)! = exp(Pi^2/6) = 5.1806683178971...

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..224

Example

E.g.f.: A(x) = 1 + 2*x^2/2! + 18*x^4/4! + 380*x^6/6! + 14980*x^8/8! +...
where
log(A(x)) = x^2 + x^4/4 + x^6/9 + x^8/16 + x^10/25 + x^12/36 + x^14/49 +...

Mathematica

nmax=20; k=2; 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)=(2*n)!*polcoeff(exp(sum(m=1, n, (x^m/m)^2)+x*O(x^(2*n))), 2*n)}
for(n=0, 20, print1(a(n), ", "))

Crossrefs

Cf. A258873, A258874.

Sequence in context: A132911 A291902 A336217 * A152684 A201732 A260656

Adjacent sequences: A226834 A226835 A226836 * A226838 A226839 A226840

Keyword

nonn

Author

Paul D. Hanna, Jun 19 2013

Status

approved