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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

Vaclav Kotesovec, Table of n, a(n) for n = 1..1000

Index entries for reversions of series

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

MATHEMATICA

nmax = 30; Rest[CoefficientList[InverseSeries[Series[Sum[PartitionsP[n]*x^n, {n, 1, nmax}], {x, 0, nmax}]], x]] (* Vaclav Kotesovec, Nov 11 2017 *)

CROSSREFS

Cf. A000041, A050393, A066398, A334315.

Sequence in context: A276721 A287583 A287276 * A007296 A279558 A224071

Adjacent sequences:  A007309 A007310 A007311 * A007313 A007314 A007315

KEYWORD

sign,easy

AUTHOR

N. J. A. Sloane, Mira Bernstein

EXTENSIONS

Signs corrected Dec 24 2001

STATUS

approved

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Last modified August 15 13:27 EDT 2020. Contains 336504 sequences. (Running on oeis4.)