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 A302582 #6 May 05 2018 05:22:34
%S A302582 0,1,3,29,386,6774,146484,3762744,111868560,3777096240,142734788640,
%T A302582 5967788097600,273488036169600,13631083378617600,734083968523046400,
%U A302582 42477063883483622400,2628184745184816384000,173147202267665649408000,12100888735302910523904000,894183767796064712795136000
%N A302582 a(n) = n! * [x^n] log(1 + x)/(1 - x)^n.
%F A302582 a(n) = n!*Sum_{k=1..n} (-1)^(k+1)*binomial(2*n-k-1,n-k)/k.
%F A302582 a(n) ~ log(3/2) * 2^(2*n - 1/2) * n^n / exp(n). - _Vaclav Kotesovec_, May 05 2018
%t A302582 Table[n! SeriesCoefficient[Log[1 + x]/(1 - x)^n, {x, 0, n}], {n, 0, 19}]
%t A302582 Table[n! Sum[(-1)^(k + 1) Binomial[2 n - k - 1, n - k]/k, {k, 1, n}], {n, 0, 19}]
%t A302582 Join[{0}, Table[n^2 (2 (n - 1))! HypergeometricPFQ[{1, 1, 1 - n}, {2, 2 - 2 n}, -1]/n!, {n, 19}]]
%Y A302582 Cf. A000254, A024167, A058806, A104150, A109792, A300489.
%K A302582 nonn
%O A302582 0,3
%A A302582 _Ilya Gutkovskiy_, Apr 10 2018