cp's OEIS Frontend

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

%I A083384 #16 Sep 08 2022 08:45:10
%S A083384 0,2,27,316,3825,49866,706923,10899512,182218005,3289724710,
%T A083384 63865092159,1327750936788,29447495757225,694257067232834,
%U A083384 17343019158929235,457695211932767344,12726295039220109885,371902424983010438238,11396594412860395106151,365458808048854606362380
%N A083384 a(n) = n*Sum(((k-1)/2)*k!*Stirling_2(n,k),k=1..n).
%F A083384 Equals A083385(n) - n*A000670(n).
%F A083384 E.g.f.: x*(exp(x)-1)*exp(x)/(2-exp(x))^3. - _Vladeta Jovovic_, Sep 14 2003
%F A083384 a(n) ~ n! * n^2 / (8 * (log(2))^(n+2)). - _Vaclav Kotesovec_, Feb 18 2017
%t A083384 a[n_] := n Sum[1/2 (k-1) k! StirlingS2[n, k], {k, 1, n}];
%t A083384 Array[a, 20] (* _Jean-François Alcover_, Sep 01 2018 *)
%t A083384 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 *)
%o A083384 (Magma) [n*&+[(k-1)/2*Factorial(k)*StirlingSecond(n, k): k in [0..n]]: n in [1..25]]; //  _Vincenzo Librandi_, Sep 01 2018
%Y A083384 Cf. A000670, A083385, A083411, A083410.
%K A083384 nonn
%O A083384 1,2
%A A083384 _N. J. A. Sloane_, Jun 07 2003