OFFSET
1,2
REFERENCES
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
Vaclav Kotesovec, Table of n, a(n) for n = 1..1000
FORMULA
From Vaclav Kotesovec, Nov 11 2017: (Start)
a(n) ~ -(-1)^n * c * d^n / n^(3/2), where
d = 5.379264118840884783404842050140885100801253519243086... and
c = 0.10697042824132534557642152089737206588353695053... (End)
G.f. A(x) satisfies: A(x) = 1 - (1/(1 + x)) * Product_{k>=2} 1/(1 - A(x)^k). - Ilya Gutkovskiy, Apr 23 2020
MAPLE
# Using function CompInv from A357588.
CompInv(25, n -> combinat:-numbpart(n)); # Peter Luschny, Oct 05 2022
MATHEMATICA
nmax = 30; Rest[CoefficientList[InverseSeries[Series[Sum[PartitionsP[n]*x^n, {n, 1, nmax}], {x, 0, nmax}]], x]] (* Vaclav Kotesovec, Nov 11 2017 *)
Rest[CoefficientList[InverseSeries[Series[-1 + 1/QPochhammer[x], {x, 0, 30}], x], x]] (* Vaclav Kotesovec, Jan 18 2024 *)
(* Calculation of constant d: *) Chop[1/r /. FindRoot[{(1 + r)*QPochhammer[s, s] == 1, Log[1 - s] + QPolyGamma[0, 1, s] - (1 + r)*s*Log[s] * Derivative[0, 1][QPochhammer][s, s] == 0}, {r, -1/5}, {s, -1/2}, WorkingPrecision -> 70]] (* Vaclav Kotesovec, Jan 18 2024 *)
CROSSREFS
KEYWORD
sign,easy
AUTHOR
EXTENSIONS
Signs corrected Dec 24 2001
STATUS
approved