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 A331689 #11 Feb 01 2020 22:55:16
%S A331689 1,3,15,103,897,9471,117703,1685475,27361953,497111707,10001175231,
%T A331689 220849928223,5312868439585,138337555830423,3876986580776247,
%U A331689 116375171226474331,3725295913465848513,126686907674290095795,4561317309742758852463,173343622143918424951767
%N A331689 E.g.f.: exp(x/(1 - x)) / (1 - 2*x).
%H A331689 Alois P. Heinz, <a href="/A331689/b331689.txt">Table of n, a(n) for n = 0..403</a>
%F A331689 a(n) = Sum_{k=0..n} binomial(n,k)^2 * k! * A000522(n-k).
%F A331689 a(n) = Sum_{k=0..n} binomial(n,k) * k! * 2^k * A000262(n-k).
%F A331689 a(n) ~ n! * exp(1) * 2^n. - _Vaclav Kotesovec_, Jan 26 2020
%p A331689 b:= proc(n) b(n):= `if`(n<0, 0, 1+n*b(n-1)) end:
%p A331689 a:= n-> n!*add(binomial(n, k)*b(k)/k!, k=0..n):
%p A331689 seq(a(n), n=0..23); # _Alois P. Heinz_, Jan 24 2020
%t A331689 nmax = 19; CoefficientList[Series[Exp[x/(1 - x)]/(1 - 2 x), {x, 0, nmax}], x] Range[0, nmax]!
%t A331689 A000522[0] = 1; A000522[n_] := Floor[Exp[1] n!]; a[n_] := Sum[Binomial[n, k]^2 k! A000522[n - k], {k, 0, n}]; Table[a[n], {n, 0, 19}]
%Y A331689 Cf. A000165, A000262, A000522, A002720, A010842, A010844, A331688.
%K A331689 nonn
%O A331689 0,2
%A A331689 _Ilya Gutkovskiy_, Jan 24 2020