A304987 G.f.: Sum_{k>=0} A000041(k) * x^k / Sum_{k>=0} A000009(k)^2 * x^k.

1, 0, 1, -2, 2, -6, 3, -16, 17, -34, 47, -78, 153, -178, 373, -530, 954, -1410, 2280, -3896, 5908, -9988, 15170, -25908, 40659, -65136, 105967, -169056, 276483, -435624, 712052, -1139814, 1839535, -2955466, 4745201, -7689672, 12303439, -19866340, 31904000

Offset: 0

Author

Vaclav Kotesovec, May 23 2018

Keywords

• sign

Crossrefs

Cf. A000009, A000041, A054440, A304877, A304990.

Programs

Mathematica

nmax = 50; CoefficientList[Series[Sum[PartitionsP[k]*x^k, {k, 0, nmax}] / Sum[PartitionsQ[k]^2*x^k, {k, 0, nmax}], {x, 0, nmax}], x]

Formula

a(n) ~ (-1)^n * c * d^n, where d = 1.6096199212376592810929072080593393678131347423108390218672748044914523428584..., c = 0.4455996319406557616008349987776746416976798533740571426884585957313974660...