cp's OEIS Frontend

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.

A299036 a(n) = [x^n] Product_{k=1..n} 1/(1-k!*x).

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%I A299036 #15 Feb 02 2018 07:00:39
%S A299036 1,1,7,381,502789,33572762781,175123095782787181,
%T A299036 99374457734129265819664221,8158897372191288496224413025490409437,
%U A299036 124778468912108975502836576328262294089846582756189
%N A299036 a(n) = [x^n] Product_{k=1..n} 1/(1-k!*x).
%H A299036 Seiichi Manyama, <a href="/A299036/b299036.txt">Table of n, a(n) for n = 0..30</a>
%F A299036 From _Vaclav Kotesovec_, Feb 02 2018: (Start)
%F A299036 a(n) ~ (n!)^n.
%F A299036 a(n) ~ 2^(n/2) * Pi^(n/2) * n^(n*(2*n+1)/2) / exp(n^2 - 1/12). (End)
%t A299036 Table[SeriesCoefficient[Product[1/(1 - k!*x), {k, 1, n}], {x, 0, n}], {n, 0, 12}] (* _Vaclav Kotesovec_, Feb 02 2018 *)
%Y A299036 Cf. A000178, A036740.
%Y A299036 Cf. A007820, A298851, A299035.
%K A299036 nonn
%O A299036 0,3
%A A299036 _Seiichi Manyama_, Feb 01 2018