A318582 Expansion of 1/(1 + x*Product_{k>=1} (1 + x^k)).

1, -1, 0, 0, -1, 1, -1, 0, 1, -1, 1, 0, 0, 1, 0, 0, 0, 1, -1, 0, 1, -3, 2, -1, -3, 4, -4, 0, 3, -5, 4, 0, -2, 4, -1, 1, 0, 3, -2, 0, 6, -11, 9, -1, -13, 18, -17, 1, 13, -23, 17, -4, -8, 13, -8, 7, -6, 15, -10, -3, 33, -50, 42, 0, -56, 85, -72, 6, 59, -100, 75, -23, -34, 53, -44, 35

Offset

0,22

Links

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

Formula

G.f.: 1/(1 + x*Sum_{k>=0} A000009(k)*x^k).

a(0) = 1; a(n) = -Sum_{k=1..n} A000009(k-1)*a(n-k).

Example

G.f. = 1 - x - x^4 + x^5 - x^6 + x^8 - x^9 + x^10 + x^13 + x^17 - x^18 + x^20 - 3*x^21 + ...

Maple

a:=series(1/(1+x*mul(1+x^k, k=1..100)), x=0, 76): seq(coeff(a, x, n), n=0..75); # Paolo P. Lava, Apr 02 2019

Mathematica

nmax = 75; CoefficientList[Series[1/(1 + x Product[(1 + x^k), {k, 1, nmax}]), {x, 0, nmax}], x]
a[0] = 1; a[n_] := a[n] = -Sum[PartitionsQ[k - 1] a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 75}]

Crossrefs

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

Cf. A000009, A081362.

Sequence in context: A102288 A081248 A214636 * A318317 A129690 A156665

Adjacent sequences: A318579 A318580 A318581 * A318583 A318584 A318585

Keyword

sign

Author

Ilya Gutkovskiy, Aug 29 2018

Status

approved