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 A295623 #15 Jul 05 2022 09:18:05
%S A295623 1,1,8,90,1424,28900,716292,20972098,708317248,27108056808,
%T A295623 1159375192100,54799938951934,2836735081572240,159606310760007436,
%U A295623 9698172715195196260,632924646574215596850,44153807025286701187328,3278903858941755472870864,258247909552273997037934788
%N A295623 a(n) = n! * [x^n] exp(n*x*exp(x)).
%H A295623 Seiichi Manyama, <a href="/A295623/b295623.txt">Table of n, a(n) for n = 0..360</a>
%H A295623 N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>
%F A295623 a(n) = n! * [x^n] exp(n*Sum_{k>=1} x^k/(k - 1)!).
%F A295623 From _Seiichi Manyama_, Jul 05 2022: (Start)
%F A295623 a(n) = [x^n] Sum_{k>=0} (n * x)^k/(1 - k*x)^(k+1).
%F A295623 a(n) = Sum_{k=0..n} n^k * k^(n-k) * binomial(n,k). (End)
%t A295623 Table[n! SeriesCoefficient[Exp[n x Exp[x]], {x, 0, n}], {n, 0, 18}]
%t A295623 Table[Sum[BellY[n, k, n Range[n]], {k, 0, n}], {n, 0, 18}]
%o A295623 (PARI) a(n) = sum(k=0, n, n^k*k^(n-k)*binomial(n, k)); \\ _Seiichi Manyama_, Jul 04 2022
%Y A295623 Cf. A000248, A242817, A275707, A351765.
%K A295623 nonn
%O A295623 0,3
%A A295623 _Ilya Gutkovskiy_, Nov 24 2017