A242228 a(n) = Sum_{k=1..n} k^(2*n-1) * k! * Stirling2(n,k).

1, 17, 1651, 473741, 300257371, 355743405917, 706872713310331, 2182548723605418941, 9894910566488309801851, 63052832687428562206049117, 545439670961897317869306191611, 6226501736967631584015448186252541, 91619831483112536750163352484302283131

Offset: 1

Author

Vaclav Kotesovec, May 08 2014

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..160

Crossrefs

Cf. A000629, A220179, A229260, A244585.

Programs

Mathematica

Table[Sum[k^(2*n-1) * k! * StirlingS2[n,k], {k,1,n}], {n,1,20}]

Formula

a(n) ~ c * d^n * (n!)^3 / n^2, where d = r^3*(1+exp(2/r)) = 7.8512435106631367719817991716164612615296980032514..., r = 0.94520217245242431308104743874492469552738... is the root of the equation (1+exp(-2/r))*LambertW(-exp(-1/r)/r) = -1/r, and c = 0.15095210978787998524366903417512193343948127919...

E.g.f.: Sum_{k>=1} (exp(k^2*x) - 1)^k / k. - Seiichi Manyama, Jun 19 2024