A227044 a(n) = Sum_{k>=1} k^(2*n)/(2^k).

1, 6, 150, 9366, 1091670, 204495126, 56183135190, 21282685940886, 10631309363962710, 6771069326513690646, 5355375592488768406230, 5149688839606380769088406, 5916558242148290945301297750, 8004451519688336984972255078166, 12595124129900132067036747870669270

Offset: 0

Author

Vaclav Kotesovec, Jun 29 2013

Keywords

• nonn

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..100

Crossrefs

Bisection of A000629.

Cf. A080163.

Programs

Mathematica

Table[Sum[k^(2*n)/(2^k), {k, 1, Infinity}], {n, 0, 20}]
a[n_] := PolyLog[-2 n, 1/2]; a[0] = 1; Array[a, 15, 0] (* Peter Luschny, Sep 06 2020 *)

PARI

{a(n) = sum(k=0, 2*n, (-2)^k * k! * stirling(2*n, k,2) )}
for(n=0, 20, print1(a(n), ", "))

Formula

a(n) ~ (2n)!/(log(2))^(2*n+1).

a(n) = Sum_{k=0..2*n} (-2)^k * k! * Stirling2(2*n, k). - Paul D. Hanna, Apr 15 2018

a(n) = A000629(2*n). - Christian Krause, Nov 22 2022