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 A331658 #35 Jan 26 2020 09:26:14
%S A331658 1,2,9,64,617,7446,107377,1795844,34114929,724822282,17018900921,
%T A331658 437402060712,12208463140249,367629791490014,11876750557295457,
%U A331658 409663873470828076,15023747377122799457,583644746007467984274,23939828792355240206569,1033788018952899566018192
%N A331658 E.g.f.: exp(x/(1 - 2*x)) / (1 - x).
%F A331658 a(n) = Sum_{k=0..n} binomial(n,k)^2 * k! * A000262(n-k).
%F A331658 a(n) = Sum_{k=0..n} binomial(n,k) * k! * A025168(n-k).
%F A331658 a(n) ~ 2^(n + 1/4) * n^(n - 1/4) * exp(-1/4 + sqrt(2*n) - n) * (1 - 23*sqrt(2) / (48*sqrt(n))). - _Vaclav Kotesovec_, Jan 26 2020
%t A331658 nmax = 19; CoefficientList[Series[Exp[x/(1 - 2 x)]/(1 - x), {x, 0, nmax}], x] Range[0, nmax]!
%t A331658 A000262[n_] := If[n == 0, 1, n! Sum[Binomial[n - 1, k]/(k + 1)!, {k, 0, n - 1}]]; a[n_] := Sum[Binomial[n, k]^2 k! A000262[n - k], {k, 0, n}]; Table[a[n], {n, 0, 19}]
%Y A331658 Cf. A000262, A002720, A025167, A025168.
%K A331658 nonn
%O A331658 0,2
%A A331658 _Ilya Gutkovskiy_, Jan 24 2020