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 A381140 #15 Feb 16 2025 08:34:07
%S A381140 1,1,3,19,161,1781,24667,409991,7959233,176920489,4432942931,
%T A381140 123648692795,3800647961761,127654261471517,4651982506605995,
%U A381140 182824074836850991,7708128977570816129,347059689259637711441,16621016953663100702755,843658152872351669816675
%N A381140 Expansion of e.g.f. exp( -LambertW(-x * cosh(x)) ).
%C A381140 As stated in the comment of A185951, A185951(n,0) = 0^n.
%H A381140 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LambertW-Function.html">Lambert W-Function</a>.
%F A381140 E.g.f. A(x) satisfies A(x) = exp( x * cosh(x) * A(x) ).
%F A381140 a(n) = Sum_{k=0..n} (k+1)^(k-1) * A185951(n,k).
%o A381140 (PARI) a185951(n, k) = binomial(n, k)/2^k*sum(j=0, k, (2*j-k)^(n-k)*binomial(k, j));
%o A381140 a(n) = sum(k=0, n, (k+1)^(k-1)*a185951(n, k));
%Y A381140 Cf. A003727, A162649, A381143.
%Y A381140 Cf. A185951.
%K A381140 nonn
%O A381140 0,3
%A A381140 _Seiichi Manyama_, Feb 15 2025