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 A357948 #29 Oct 29 2022 09:37:59 %S A357948 1,1,1,-5,-23,1,601,2731,-13775,-219743,-313199,15383611,125451481, %T A357948 -811558175,-20767068503,-37852036949,2898343066081,28990920216001, %U A357948 -313289894357855,-8634009894555653,-3214642669500599,2108734127922999361,20183394611962437241 %N A357948 Expansion of e.g.f. exp( x * exp(-x^2) ). %F A357948 a(n) = n! * Sum_{k=0..floor(n/2)} (-n + 2*k)^k/(k! * (n - 2*k)!). %o A357948 (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(x*exp(-x^2)))) %o A357948 (PARI) a(n) = n!*sum(k=0, n\2, (-n+2*k)^k/(k!*(n-2*k)!)); %Y A357948 Cf. A003725, A358063. %Y A357948 Cf. A216688. %K A357948 sign,easy %O A357948 0,4 %A A357948 _Seiichi Manyama_, Oct 29 2022