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 A308538 #5 Jun 06 2019 21:59:53
%S A308538 1,-1,3,-11,-47,2111,-18589,-671803,24578625,328227551,-44122149981,
%T A308538 -17436709707,129678315723089,-1671362093527073,-621466693739336509,
%U A308538 16245508786340273349,4705502566521408713473,-172007688705762528111809,-54084940569279187064459581
%N A308538 a(n) = exp(1) * Sum_{k>=0} (-1)^k*(k*(k + 1))^n/k!.
%F A308538 a(n) = Sum_{k=0..n} binomial(n,k)*A000587(2*n-k).
%t A308538 Table[Exp[1] Sum[(-1)^k (k (k + 1))^n/k!, {k, 0, Infinity}], {n, 0, 18}]
%t A308538 Table[Sum[Binomial[n, k] BellB[2 n - k, -1], {k, 0, n}], {n, 0, 18}]
%Y A308538 Cf. A000587, A020556, A090211, A094577.
%K A308538 sign
%O A308538 0,3
%A A308538 _Ilya Gutkovskiy_, Jun 06 2019