A308865 a(n) = Sum_{k>=0} k^(2*n+1)/2^(k+1).

1, 13, 541, 47293, 7087261, 1622632573, 526858348381, 230283190977853, 130370767029135901, 92801587319328411133, 81124824998504073881821, 85438451336745709294580413, 106697365438475775825583498141, 155897763918621623249276226253693, 263478385263023690020893329044576861

Offset: 0

Author

Ilya Gutkovskiy, Jun 29 2019

Keywords

• nonn

Crossrefs

Cf. A000670, A008277, A099977, A249938.

Programs

Mathematica

Table[Sum[k^(2 n + 1)/2^(k + 1), {k, 0, Infinity}], {n, 0, 14}]
Table[Sum[k! StirlingS2[2 n + 1, k], {k, 0, 2 n + 1}], {n, 0, 14}]

Formula

a(n) = Sum_{k=0..2*n+1} k!*Stirling2(2*n+1,k).

a(n) = A000670(2*n+1).

a(n) ~ sqrt(Pi) * 2^(2*n + 1) * n^(2*n + 3/2) / (exp(2*n) * (log(2))^(2*n + 2)). - Vaclav Kotesovec, Sep 25 2019