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 A294468 #16 Oct 15 2018 22:19:47
%S A294468 1,0,1,8,9,224,1225,11304,103537,1431296,15642801,206721800,
%T A294468 3295533241,47467875168,859354139449,15596241280424,283240963555425,
%U A294468 5859309797252864,129874369387025377,2752905169704533256,67640333903657850601
%N A294468 Inverse binomial transform of A088311.
%H A294468 G. C. Greubel, <a href="/A294468/b294468.txt">Table of n, a(n) for n = 0..443</a>
%F A294468 a(n) = Sum_{k=0..n} (-1)^(n-k) * binomial(n,k) * A088311(k).
%F A294468 a(n) ~ exp(-1) * n! * A000009(n).
%F A294468 a(n) ~ sqrt(2*Pi) * exp(Pi*sqrt(n/3) - n - 1) * n^(n - 1/4) / (4*3^(1/4)).
%F A294468 E.g.f.: exp(-x) * Product_{k>=1} (1 + x^k). - _Ilya Gutkovskiy_, Oct 15 2018
%t A294468 Table[Sum[(-1)^(n-k)*Binomial[n, k]*k!*PartitionsQ[k], {k, 0, n}], {n, 0, 20}]
%t A294468 max = 20; t = Table[k!*PartitionsQ[k], {k, 0, max}]; Table[Differences[t, n], {n, 0, max}][[All, 1]] (* _Jean-François Alcover_, Nov 02 2017 *)
%Y A294468 Cf. A266232, A294467, A293467.
%Y A294468 Cf. A218481, A294466, A281425, A095051.
%K A294468 nonn
%O A294468 0,4
%A A294468 _Vaclav Kotesovec_, Oct 31 2017