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.

A335227 G.f.: x / (Sum_{k>=1} k * x^k / (1 + x^k)).

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%I A335227 #5 May 27 2020 20:16:31
%S A335227 1,-1,-3,6,1,-20,24,38,-132,34,411,-632,-601,2914,-1664,-7822,15649,
%T A335227 6802,-62082,55672,141109,-369310,-12036,1275642,-1580834,-2343886,
%U A335227 8375349,-2648282,-25217490,41097852,33815048,-183252284,117569579,475949186,-1006346968,-344955964
%N A335227 G.f.: x / (Sum_{k>=1} k * x^k / (1 + x^k)).
%F A335227 G.f.: x / (Sum_{k>=1} (-1)^(k+1) * x^k / (1 - x^k)^2).
%F A335227 G.f.: 1 / log(g(x))', where g(x) = Product_{k>=1} (1 + x^k) is the g.f. for A000009.
%F A335227 G.f.: 1 / (Sum_{k>=0} A000593(k+1) * x^k).
%F A335227 a(0) = 1; a(n) = -Sum_{k=1..n} A000593(k+1) * a(n-k).
%t A335227 nmax = 35; CoefficientList[Series[x/Sum[k x^k/(1 + x^k), {k, 1, nmax + 1}], {x, 0, nmax}], x]
%t A335227 nmax = 35; CoefficientList[Series[1/D[Log[Product[(1 + x^k), {k, 1, nmax + 1}]], x], {x, 0, nmax}], x]
%t A335227 a[0] = 1; a[n_] := a[n] = -Sum[DivisorSum[k + 1, # &, OddQ[#] &] a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 35}]
%Y A335227 Cf. A000009, A000593, A002039, A180305, A320651, A335228.
%K A335227 sign
%O A335227 0,3
%A A335227 _Ilya Gutkovskiy_, May 27 2020