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 A375810 #12 Sep 01 2024 10:13:59 %S A375810 1,2,6,30,192,1480,13500,141540,1676640,22141728,322388640,5130084960, %T A375810 88561408320,1648294876800,32898981155040,700940855815200, %U A375810 15877318955097600,380996919471168000,9654670629548904960,257627854786123261440,7220676423560766566400 %N A375810 Expansion of e.g.f. 1/(1 - (exp(x^2) - 1)/x)^2. %F A375810 E.g.f.: B(x)^2, where B(x) is the e.g.f. of A375795. %F A375810 a(n) = n! * Sum_{k=0..floor(n/2)} (n-2*k+1)! * Stirling2(n-k,n-2*k)/(n-k)!. %o A375810 (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1-(exp(x^2)-1)/x)^2)) %o A375810 (PARI) a(n) = n!*sum(k=0, n\2, (n-2*k+1)!*stirling(n-k, n-2*k, 2)/(n-k)!); %Y A375810 Cf. A375795, A375811. %Y A375810 Cf. A375664. %K A375810 nonn %O A375810 0,2 %A A375810 _Seiichi Manyama_, Aug 29 2024