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 A380406 #15 Aug 05 2025 07:15:40
%S A380406 1,2,12,104,1232,18592,342208,7451264,187631872,5369721344,
%T A380406 172255038464,6125052946432,239195824279552,10179739052908544,
%U A380406 469024768235192320,23263095316577681408,1235978286454556131328,70040404736026578386944,4217180561907991530176512
%N A380406 E.g.f. satisfies A(x) = exp( 2 * x * exp(x) * A(x)^(1/2) ).
%H A380406 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LambertW-Function.html">Lambert W-Function</a>.
%F A380406 E.g.f.: B(x)^2, where B(x) is the e.g.f. of A273954.
%F A380406 E.g.f.: A(x) = exp( -2*LambertW(-x * exp(x)) ).
%F A380406 a(n) = 2 * Sum_{k=0..n} k^(n-k) * (k+2)^(k-1) * binomial(n,k).
%F A380406 a(n) ~ 2 * sqrt(1 + LambertW(exp(-1))) * n^(n-1) / (exp(n-2) * LambertW(exp(-1))^n). - _Vaclav Kotesovec_, Aug 05 2025
%o A380406 (PARI) a(n) = 2*sum(k=0, n, k^(n-k)*(k+2)^(k-1)*binomial(n, k));
%Y A380406 Cf. A273954, A357247, A380407.
%Y A380406 Cf. A273953, A360473.
%K A380406 nonn
%O A380406 0,2
%A A380406 _Seiichi Manyama_, Jan 23 2025