A097656 Binomial transform of A038507.

2, 4, 9, 24, 81, 358, 2021, 13828, 109857, 986922, 9865125, 108507160, 1302065441, 16926805678, 236975181189, 3554627504844, 56874039618753, 966858672535762, 17403456103546565, 330665665962928288, 6613313319249128577

Offset

0,1

Links

Table of n, a(n) for n=0..20.

Formula

a(n) = Sum_{k=0..n) n!(k!+1) / k!(n-k)! = Sum_{k=0..n} (P(n, k) + C(n, k)) = Sum_{k=0..n} P(n, k) + 2^n = A007526(n) + A000079(n). - Ross La Haye, Aug 24 2006

Example

a(2) = 9 because P(2,0) = 1, P(2,1) = 2, P(2,2) = 2 while C(2,0) = 1, C(2,1) = 2, C(2,2) = 1 and 1 + 1 + 2 + 2 + 2 + 1 = 9.

Mathematica

f[n_] := Sum[n!(k! + 1)/(k!(n - k)!), {k, 0, n}]; Table[ f[n], {n, 0, 20}] (* Robert G. Wilson v, Sep 24 2004 *)

Crossrefs

Cf. A038507, A097204.

Sequence in context: A137154 A098448 A006406 * A324148 A012936 A013091

Adjacent sequences: A097653 A097654 A097655 * A097657 A097658 A097659

Keyword

nonn

Author

Ross La Haye, Sep 20 2004

Status

approved