A318581 Expansion of 1/(1 + x*Product_{k>=1} 1/(1 - x^k)).

1, -1, 0, -1, 0, -1, 1, -1, 3, -1, 5, -2, 7, -7, 9, -16, 11, -29, 20, -46, 45, -66, 94, -95, 175, -161, 294, -307, 458, -594, 715, -1096, 1193, -1891, 2132, -3106, 3916, -5063, 7083, -8484, 12347, -14770, 20867, -26310, 34898, -46771, 58967, -81665, 101680, -139951, 178094, -237620

Offset

0,9

Links

Seiichi Manyama, Table of n, a(n) for n = 0..5000

Formula

G.f.: 1/(1 + x*Sum_{k>=0} A000041(k)*x^k).

a(0) = 1; a(n) = -Sum_{k=1..n} A000041(k-1)*a(n-k).

Example

G.f. = 1 - x - x^3 - x^5 + x^6 - x^7 + 3*x^8 - x^9 + 5*x^10 - 2*x^11 + 7*x^12 - 7*x^13 + ...

Maple

seq(coeff(series((1+x*mul((1-x^k)^(-1), k=1..n))^(-1), x, n+1), x, n), n = 0 .. 55); # Muniru A Asiru, Aug 30 2018

Mathematica

nmax = 51; CoefficientList[Series[1/(1 + x Product[1/(1 - x^k), {k, 1, nmax}]), {x, 0, nmax}], x]
a[0] = 1; a[n_] := a[n] = -Sum[PartitionsP[k - 1] a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 51}]

Crossrefs

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

Cf. A000041, A010815.

Sequence in context: A174239 A066249 A065168 * A065277 A249139 A059971

Adjacent sequences: A318578 A318579 A318580 * A318582 A318583 A318584

Keyword

sign

Author

Ilya Gutkovskiy, Aug 29 2018

Status

approved