This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A097656 #11 Aug 29 2024 21:03:00
%S A097656 2,4,9,24,81,358,2021,13828,109857,986922,9865125,108507160,
%T A097656 1302065441,16926805678,236975181189,3554627504844,56874039618753,
%U A097656 966858672535762,17403456103546565,330665665962928288,6613313319249128577
%N A097656 Binomial transform of A038507.
%F A097656 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 A097656 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 A097656 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 A097656 Cf. A038507, A097204.
%K A097656 nonn
%O A097656 0,1
%A A097656 _Ross La Haye_, Sep 20 2004