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%I #8 Jul 26 2015 04:09:09
%S 2,4,9,24,81,358,2021,13828,109857,986922,9865125,108507160,
%T 1302065441,16926805678,236975181189,3554627504844,56874039618753,
%U 966858672535762,17403456103546565,330665665962928288,6613313319249128577
%N Binomial transform of A038507.
%F 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
%e 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.
%t 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 *)
%Y Cf. A038507, A097204.
%K nonn
%O 0,1
%A _Ross La Haye_, Sep 20 2004
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