A114633 a(n) = (n+1)*(n+2)/2 * Sum_{k=0..floor(n/2)} n!/(n-2*k)!.

1, 3, 18, 70, 555, 2961, 31108, 213228, 2799765, 23455135, 369569046, 3659001138, 67261566463, 768390239085, 16142775951240, 209002145031256, 4939689441079593, 71478733600689723, 1877081987610245530, 30021068112289683870, 867211878275933435091, 15190660464818580038473

Offset: 0

Author

Creighton Dement, Feb 17 2006

Keywords

• nonn

Comments

Formula was found by Paul D. Hanna.

Related to logarithmic numbers A002104.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..450

Crossrefs

Cf. A002104, A087208.

Programs

Maple

a:= n-> (n+1)*(n+2)/2*sum(n!/(n-2*k)!,k=0..floor(n/2)): seq(a(n), n=0..20);

Mathematica

Rest[Rest[With[{nn=25}, CoefficientList[Series[Exp[x]/(1 - x^2)(x^2/2), {x, 0, nn}], x] Range[0, nn]!]]] (* Vincenzo Librandi, Sep 03 2017 *)

Formula

a(n) = A087208(n)*(n+1)*(n+2)/2. - Paul D. Hanna

E.g.f.: exp(x)/(1-x^2)*(x^2/2) (with offset 2). - Zerinvary Lajos, Apr 03 2009

Extensions

More terms from Vincenzo Librandi, Sep 03 2017