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A066398 Reversion of g.f. (with constant term included) for partition numbers. 6
1, -1, 0, 2, -3, 0, 5, 0, -21, 14, 117, -342, 210, 935, -2565, 1864, 2751, -3945, -8074, 4046, 108927, -333832, 246895, 887040, -2764795, 3062749, -1372098, 4775900, -9367698, -55130625, 299939766, -537241936, -140898285, 2464380030, -4060507784, 193070394 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

See A301624 for the corresponding series reversion for the plane partition numbers A000219. - Peter Bala, Feb 09 2020

LINKS

Table of n, a(n) for n=0..35.

P. Bala, Representing a sequence as [x^n] G(x)^n

Index entries for reversions of series

FORMULA

The o.g.f. A(x) = 1 - x + 2*x^3 - 3*x^4 + 5*x^6 - ... satisfies [x^n](1/A(x))^n = sigma(n) = A000203(n) for n >= 1. - Peter Bala, Aug 23 2015

G.f. A(x) satisfies: A(x) = Product_{k>=1} (1 - x^k*A(x)^k). - Ilya Gutkovskiy, Mar 21 2018

MAPLE

with(numtheory):

Order := 36:

Gser := solve(series(x*exp(add(sigma[1](n)*x^n/n, n = 1..35)), x) = y, x):

seq(coeff(Gser, y^k), k = 1..35); # Peter Bala, Feb 09 2020

MATHEMATICA

nmax = 34; sol = {a[0] -> 1};

Do[A[x_] = Sum[a[k] x^k, {k, 0, n}] /. sol; eq = CoefficientList[A[x] - Product[ 1 - x^k*A[x]^k, {k, 1, n}] + O[x]^(n + 1), x] == 0 /. sol; sol = sol ~Join~ Solve[eq][[1]], {n, 1, nmax}];

sol /. Rule -> Set;

a /@ Range[0, nmax] (* Jean-Fran├žois Alcover, Nov 02 2019 *)

CROSSREFS

Cf. A000041, A000203, A007312, A301624.

Sequence in context: A082809 A070245 A243868 * A138197 A140664 A335940

Adjacent sequences:  A066395 A066396 A066397 * A066399 A066400 A066401

KEYWORD

sign

AUTHOR

N. J. A. Sloane, Dec 25 2001

STATUS

approved

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Last modified October 22 15:25 EDT 2021. Contains 348172 sequences. (Running on oeis4.)