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A109084 G.f. A(x) satisfies: A(x) = 1/G000041(x/A(x)) where G000041(x) is the g.f. of the partition numbers A000041. 4
1, -1, -2, -5, -17, -63, -253, -1062, -4615, -20570, -93538, -432211, -2023567, -9578815, -45767162, -220431025, -1069079067, -5216655257, -25592441875, -126157044454, -624560659184, -3103962569509, -15480272621533, -77450458331100, -388627340240958, -1955249529839424 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Note: coefficient [x^n] A(x)^n = -A000203(n) (sum of divisors of n) for n>0.

LINKS

Vaclav Kotesovec, Table of n, a(n) for n = 0..1000

FORMULA

G.f.: A(x) = x/series_reversion(x*eta(x)). G.f.: A(x) = 1/G109085(x) where G109085(x) is g.f. of A109085.

a(n) ~ -c * d^n / n^(3/2), where d = A270915 = 5.35270133348664268777241581416... and c = 0.146705445870000769931272287955221766131167... - Vaclav Kotesovec, May 13 2018

EXAMPLE

The initial terms [x^0] through [x^n] of n-th self-convolution

are persistently small:

A^0: 1;

A^1: 1,-1;

A^2: 1,-2,-3;

A^3: 1,-3,-3,-4;

A^4: 1,-4,-2,0,-7;

A^5: 1,-5,0,5,0,-6;

A^6: 1,-6,3,10,3,6,-12;

A^7: 1,-7,7,14,0,7,0,-8;

A^8: 1,-8,12,16,-10,0,-8,8,-15;

A^9: 1,-9,18,15,-27,-9,-21,0,0,-13;

PROG

(PARI) a(n)=polcoeff(x/serreverse(x*eta(x+x*O(x^n))), n)

CROSSREFS

Cf. A109085, A000041, A000203.

Sequence in context: A148416 A259792 A003456 * A217596 A090902 A150012

Adjacent sequences:  A109081 A109082 A109083 * A109085 A109086 A109087

KEYWORD

sign

AUTHOR

Paul D. Hanna, Jun 18 2005

STATUS

approved

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Last modified July 15 14:07 EDT 2019. Contains 325030 sequences. (Running on oeis4.)