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

Author

Ross La Haye, Sep 20 2004

Keywords

• nonn

Examples

			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.
		

Crossrefs

Cf. A038507, A097204.

Programs

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 *)

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