A299208 Expansion of 1/(1 - x*Product_{k>=1} 1/(1 + x^k)).

1, 1, 0, -1, -2, -1, 1, 3, 3, 1, -3, -6, -5, 1, 9, 12, 5, -9, -20, -18, 1, 26, 38, 21, -21, -61, -62, -9, 72, 120, 81, -44, -177, -205, -64, 186, 366, 293, -63, -496, -657, -304, 445, 1084, 1014, 33, -1341, -2053, -1238, 959, 3132, 3378, 770, -3474, -6260, -4619, 1656, 8809, 10929, 4306, -8520

Offset

0,5

Links

Seiichi Manyama, Table of n, a(n) for n = 0..10000

N. J. A. Sloane, Transforms

Formula

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

a(0) = 1; a(n) = Sum_{k=1..n} A081362(k-1)*a(n-k).

Mathematica

nmax = 60; CoefficientList[Series[1/(1 - x Product[1/(1 + x^k), {k, 1, nmax}]), {x, 0, nmax}], x]

Crossrefs

Antidiagonal sums of A286352.

Cf. similar sequences: A067687, A299105, A299106, A299208, A302017, A318581, A318582, A331484.

Cf. A081362, A299108, A299162, A299164, A299166, A299167, A299209, A299210, A299211, A299212.

Sequence in context: A029264 A215064 A124054 * A334187 A082870 A026009

Adjacent sequences: A299205 A299206 A299207 * A299209 A299210 A299211

Keyword

sign

Author

Ilya Gutkovskiy, Feb 05 2018

Status

approved