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.

A319754 a(n) = [x^n] Product_{k>=1} (1 - x^k)/(1 - n*x^k).

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%I A319754 #10 Dec 06 2020 04:51:25
%S A319754 1,0,3,24,252,3096,46620,823152,16776648,387413208,9999989010,
%T A319754 285311493720,8916100178843,302875101365928,11112006817455180,
%U A319754 437893890197853824,18446744073423298800,827240261878925204256,39346408075284871499214,1978419655659972977219880
%N A319754 a(n) = [x^n] Product_{k>=1} (1 - x^k)/(1 - n*x^k).
%H A319754 Seiichi Manyama, <a href="/A319754/b319754.txt">Table of n, a(n) for n = 0..386</a>
%F A319754 a(n) = [x^n] exp(Sum_{k>=1} ( Sum_{d|k} d*(n^(k/d) - 1) ) * x^k/k).
%F A319754 a(n) ~ n^n. - _Vaclav Kotesovec_, Sep 27 2018
%t A319754 Table[SeriesCoefficient[Product[(1 - x^k)/(1 - n x^k), {k, 1, n}], {x, 0, n}], {n, 0, 19}]
%t A319754 Table[SeriesCoefficient[Exp[Sum[Sum[d (n^(k/d) - 1), {d, Divisors[k]}] x^k/k, {k, 1, n}]], {x, 0, n}], {n, 0, 19}]
%Y A319754 Main diagonal of A319753.
%K A319754 nonn
%O A319754 0,3
%A A319754 _Ilya Gutkovskiy_, Sep 27 2018