A083384 a(n) = n*Sum(((k-1)/2)*k!*Stirling_2(n,k),k=1..n).

0, 2, 27, 316, 3825, 49866, 706923, 10899512, 182218005, 3289724710, 63865092159, 1327750936788, 29447495757225, 694257067232834, 17343019158929235, 457695211932767344, 12726295039220109885, 371902424983010438238, 11396594412860395106151, 365458808048854606362380

Offset: 1

Author

N. J. A. Sloane, Jun 07 2003

Keywords

• nonn

Crossrefs

Cf. A000670, A083385, A083411, A083410.

Programs

Magma

[n*&+[(k-1)/2*Factorial(k)*StirlingSecond(n, k): k in [0..n]]: n in [1..25]]; //  Vincenzo Librandi, Sep 01 2018

Mathematica

a[n_] := n Sum[1/2 (k-1) k! StirlingS2[n, k], {k, 1, n}];
Array[a, 20] (* Jean-François Alcover, Sep 01 2018 *)
Rest[Range[0, 19]! CoefficientList[Series[x (Exp[x] - 1) Exp[x] / (2 - Exp[x])^3, {x, 0, 19}], x]] (* Vincenzo Librandi, Sep 01 2018 *)

Formula

Equals A083385(n) - n*A000670(n).

E.g.f.: x*(exp(x)-1)*exp(x)/(2-exp(x))^3. - Vladeta Jovovic, Sep 14 2003

a(n) ~ n! * n^2 / (8 * (log(2))^(n+2)). - Vaclav Kotesovec, Feb 18 2017