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 A377599 #82 Feb 16 2025 08:34:07
%S A377599 1,2,13,145,2277,46461,1172713,35374697,1243296169,49940748073,
%T A377599 2258238723021,113567169318285,6289161888870061,380364426242671469,
%U A377599 24948313525570134001,1764095427822803465521,133782341347522663175889,10832097536377585282160337,932693691617428946786304661
%N A377599 E.g.f. satisfies A(x) = exp( x * A(x) / (1-x)^2 ) / (1-x).
%H A377599 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LambertW-Function.html">Lambert W-Function</a>.
%F A377599 E.g.f.: exp( -LambertW(-x/(1-x)^3) )/(1-x).
%F A377599 a(n) = n! * Sum_{k=0..n} (k+1)^(k-1) * binomial(n+2*k,n-k)/k!.
%o A377599 (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(-lambertw(-x/(1-x)^3))/(1-x)))
%o A377599 (PARI) a(n) = n!*sum(k=0, n, (k+1)^(k-1)*binomial(n+2*k, n-k)/k!);
%Y A377599 Cf. A367789, A377608, A377811.
%Y A377599 Cf. A361599.
%K A377599 nonn
%O A377599 0,2
%A A377599 _Seiichi Manyama_, Nov 14 2024