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A227044
a(n) = Sum_{k>=1} k^(2*n)/(2^k).
1
1, 6, 150, 9366, 1091670, 204495126, 56183135190, 21282685940886, 10631309363962710, 6771069326513690646, 5355375592488768406230, 5149688839606380769088406, 5916558242148290945301297750, 8004451519688336984972255078166, 12595124129900132067036747870669270
OFFSET
0,2
LINKS
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
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 *)
PROG
(PARI) {a(n) = sum(k=0, 2*n, (-2)^k * k! * stirling(2*n, k, 2) )}
for(n=0, 20, print1(a(n), ", "))
CROSSREFS
Bisection of A000629.
Cf. A080163.
Sequence in context: A013296 A013301 A233734 * A188420 A089482 A126679
KEYWORD
nonn
AUTHOR
Vaclav Kotesovec, Jun 29 2013
STATUS
approved