A335227 -id:A335227 - cp's OEIS frontend

A335228 G.f.: x / (Sum_{k>=1} x^k / (1 + x^k)^2).

1, 1, -3, -2, 9, 0, -32, 18, 108, -118, -333, 576, 911, -2466, -2040, 9702, 2529, -35622, 8254, 122436, -88275, -391882, 501660, 1148334, -2331810, -2949282, 9689949, 5791930, -37155906, -2645148, 133051344, -54698868, -445531893, 408566282, 1383325848, -2115234972

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Ilya Gutkovskiy, May 27 2020

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Cf. A002039, A002129, A010054, A180305, A335227.

nmax = 35; CoefficientList[Series[x/Sum[x^k/(1 + x^k)^2, {k, 1, nmax + 1}], {x, 0, nmax}], x]
nmax = 35; CoefficientList[Series[1/D[Log[Sum[x^(k (k + 1)/2), {k, 0, nmax}]], x], {x, 0, nmax}], x]
a[0] = 1; a[n_] := a[n] = -Sum[DivisorSum[k + 1, (-1)^(# + 1) # &] a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 35}]

G.f.: x / (Sum_{k>=1} (-1)^(k+1) * k * x^k / (1 - x^k)).
G.f.: 1 / log(g(x))', where g(x) = Sum_{k>=0} x^(k*(k + 1)/2) is the g.f. for A010054.
G.f.: 1 / (Sum_{k>=0} A002129(k+1) * x^k).
a(0) = 1; a(n) = -Sum_{k=1..n} A002129(k+1) * a(n-k).

cp's OEIS Frontend

A335228 G.f.: x / (Sum_{k>=1} x^k / (1 + x^k)^2).

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