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 A302583 #5 Apr 10 2018 14:17:39
%S A302583 0,1,4,28,272,3376,51012,908608,18640960,432891136,11225320100,
%T A302583 321504185344,10079828372880,343360783937536,12627774819845668,
%U A302583 498676704524517376,21046391759976988928,945381827279671853056,45032132922921758270916,2267322327322331161821184
%N A302583 a(n) = ((n + 1)^n - (n - 1)^n)/2.
%H A302583 N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>
%F A302583 E.g.f.: (x^2 - LambertW(-x)^2)/(2*x*LambertW(-x)*(1 + LambertW(-x))).
%F A302583 a(n) = n! * [x^n] exp(n*x)*sinh(x).
%t A302583 Table[((n + 1)^n - (n - 1)^n)/2, {n, 0, 19}]
%t A302583 nmax = 19; CoefficientList[Series[(x^2 - LambertW[-x]^2)/(2 x LambertW[-x] (1 + LambertW[-x])), {x, 0, nmax}], x] Range[0, nmax]!
%t A302583 Table[n! SeriesCoefficient[Exp[n x] Sinh[x], {x, 0, n}], {n, 0, 19}]
%Y A302583 Cf. A000169, A065440, A007778, A062024, A115416, A274278, A293022, A302584, A302585, A302586, A302587.
%K A302583 nonn
%O A302583 0,3
%A A302583 _Ilya Gutkovskiy_, Apr 10 2018