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 A375795 #10 Aug 29 2024 11:24:47 %S A375795 1,1,2,9,48,320,2580,24150,258720,3117744,41741280,614774160, %T A375795 9877412160,171923225760,3222634615200,64721762305200, %U A375795 1386495651340800,31558444491974400,760564843136017920,19348085890139086080,518103061345155686400,14567452481227893811200 %N A375795 Expansion of e.g.f. 1/(1 - (exp(x^2) - 1)/x). %F A375795 a(n) = n! * Sum_{k=0..floor(n/2)} (n-2*k)! * Stirling2(n-k,n-2*k)/(n-k)!. %o A375795 (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1-(exp(x^2)-1)/x))) %o A375795 (PARI) a(n) = n!*sum(k=0, n\2, (n-2*k)!*stirling(n-k, n-2*k, 2)/(n-k)!); %Y A375795 Cf. A000670, A375796. %Y A375795 Cf. A357962. %K A375795 nonn %O A375795 0,3 %A A375795 _Seiichi Manyama_, Aug 29 2024