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 A375897 #14 Aug 27 2025 04:59:37
%S A375897 1,2,12,122,1780,34082,810740,23093562,767175972,29140904402,
%T A375897 1246366394548,59292772664666,3106206974812292,177715679350850370,
%U A375897 11026719500616041076,737552919428497318394,52907911316906095281508,4051998061642112552244722
%N A375897 E.g.f. satisfies A(x) = 1 / (2 - exp(x * A(x)^(1/2)))^2.
%F A375897 E.g.f.: B(x)^2, where B(x) is the e.g.f. of A052894.
%F A375897 E.g.f.: A(x) = ( (1/x) * Series_Reversion(x * (2 - exp(x))) )^2.
%F A375897 a(n) = (2/(n+2)!) * Sum_{k=0..n} (n+k+1)! * Stirling2(n,k).
%F A375897 a(n) ~ LambertW(2*exp(1))^(n+2) * n^(n-1) / (2^(n+1) * exp(n) * sqrt(LambertW(2*exp(1)) + 1) * (LambertW(2*exp(1)) - 1)^(2*n+2)). - _Vaclav Kotesovec_, Aug 27 2025
%t A375897 Table[2/(n+2)! * Sum[(n + k + 1)!*StirlingS2[n, k], {k, 0, n} ], {n, 0, 20}] (* _Vaclav Kotesovec_, Aug 27 2025 *)
%o A375897 (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace((serreverse(x*(2-exp(x)))/x)^2))
%o A375897 (PARI) a(n) = 2*sum(k=0, n, (n+k+1)!*stirling(n, k, 2))/(n+2)!;
%Y A375897 Cf. A052894, A375898.
%Y A375897 Cf. A005649.
%K A375897 nonn,changed
%O A375897 0,2
%A A375897 _Seiichi Manyama_, Sep 01 2024