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 A380015 #10 Jan 23 2025 04:42:09
%S A380015 1,1,5,36,361,4640,72771,1347598,28778849,696288888,18823644595,
%T A380015 562350743306,18397666000209,654164843763340,25118967828553067,
%U A380015 1035914449832324070,45665488606439586241,2142825945301659242576,106641225471890568771747,5610282675990428302440130
%N A380015 Expansion of e.g.f. 1/sqrt(1 - 2*x*exp(x)).
%F A380015 a(n) = n! * Sum_{k=0..n} (-2)^k * k^(n-k) * binomial(-1/2,k)/(n-k)!.
%F A380015 a(n) ~ sqrt(2) * n^n / (sqrt(1 + LambertW(1/2)) * exp(n) * LambertW(1/2)^n). - _Vaclav Kotesovec_, Jan 23 2025
%o A380015 (PARI) a(n) = n!*sum(k=0, n, (-2)^k*k^(n-k)*binomial(-1/2, k)/(n-k)!);
%Y A380015 Cf. A006153, A380017, A380019.
%K A380015 nonn
%O A380015 0,3
%A A380015 _Seiichi Manyama_, Jan 09 2025