login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A007312 Reversion of g.f. (with constant term omitted) for partition numbers.
(Formerly M1482)
11
1, -2, 5, -15, 52, -200, 825, -3565, 15900, -72532, 336539, -1582593, 7524705, -36111810, 174695712, -851020367, 4171156249, -20555470155, 101787990805, -506227992092, 2527493643612, -12663916942984, 63656297034920, -320914409885850, 1622205233276889 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
REFERENCES
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
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
Sequence in context: A369443 A369398 A370798 * A007296 A279558 A224071
KEYWORD
sign,easy
AUTHOR
EXTENSIONS
Signs corrected Dec 24 2001
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified June 22 15:19 EDT 2024. Contains 373587 sequences. (Running on oeis4.)