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 A375832 #8 Aug 31 2024 06:39:47
%S A375832 1,0,0,6,0,60,1440,1680,100800,1905120,9979200,427109760,8103110400,
%T A375832 102745843200,3926897694720,84531807360000,1844343928627200,
%U A375832 69047821979136000,1790206583413248000,54550224714585600000,2112795340044060672000
%N A375832 E.g.f. satisfies A(x) = 1/(1 + x*log(1 - x^2*A(x))).
%F A375832 a(n) = n! * Sum_{k=0..floor(n/2)} (n-k)! * |Stirling1(k,n-2*k)|/( k! * (k+1)! ).
%F A375832 a(n) ~ sqrt(s*(-1 + s*(1 + r^2 + r^2*(-1 + 2*r)*s))/(1 + 2*r*s)) * n^(n-1) / (exp(n) * r^(n+1)), where r = 0.555108855597239653157700556001479889170962... and s = 1.679468515326835651547953595104045902497719... are real roots of the system of equations 1 + r*log(1 - r^2*s) = 1/s, r^3*s^2 = 1 - r^2*s. - _Vaclav Kotesovec_, Aug 31 2024
%t A375832 Table[n!*Sum[(n-k)!*Abs[StirlingS1[k, n - 2*k]]/(k!*(k + 1)!), {k, 0, Floor[n/2]}], {n, 0, 20}] (* _Vaclav Kotesovec_, Aug 31 2024 *)
%o A375832 (PARI) a(n) = n!*sum(k=0, n\2, (n-k)!*abs(stirling(k, n-2*k, 1))/(k!*(k+1)!));
%Y A375832 Cf. A371302.
%K A375832 nonn
%O A375832 0,4
%A A375832 _Seiichi Manyama_, Aug 30 2024