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

1, -1, -3, 6, 1, -20, 24, 38, -132, 34, 411, -632, -601, 2914, -1664, -7822, 15649, 6802, -62082, 55672, 141109, -369310, -12036, 1275642, -1580834, -2343886, 8375349, -2648282, -25217490, 41097852, 33815048, -183252284, 117569579, 475949186, -1006346968, -344955964

Offset

0,3

Links

Table of n, a(n) for n=0..35.

Formula

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

G.f.: 1 / log(g(x))', where g(x) = Product_{k>=1} (1 + x^k) is the g.f. for A000009.

G.f.: 1 / (Sum_{k>=0} A000593(k+1) * x^k).

a(0) = 1; a(n) = -Sum_{k=1..n} A000593(k+1) * a(n-k).

Mathematica

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

Crossrefs

Cf. A000009, A000593, A002039, A180305, A320651, A335228.

Sequence in context: A108441 A176231 A176230 * A094445 A004158 A221705

Adjacent sequences: A335224 A335225 A335226 * A335228 A335229 A335230

Keyword

sign

Author

Ilya Gutkovskiy, May 27 2020

Status

approved