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A022726 Expansion of 1/Product_{m>=1} (1 - m*q^m)^2. 3
1, 2, 7, 18, 49, 114, 282, 624, 1422, 3058, 6597, 13700, 28564, 57698, 116479, 230398, 453698, 879080, 1696732, 3230578, 6124326, 11486884, 21439480, 39659598, 73036175, 133445640, 242756058, 438680734, 789328034, 1411926186, 2515574329, 4458203590, 7871211452, 13831782146 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Self-convolution of A006906. - Vaclav Kotesovec, Jan 06 2016

LINKS

Vaclav Kotesovec, Table of n, a(n) for n = 0..6000

FORMULA

From Vaclav Kotesovec, Jan 07 2016: (Start)

a(n) ~ c * n * 3^(n/3), where

c = 9588921272.54120308291761424720457... = (c0^2 + 2*c1*c2)/3  if mod(n,3)=0

c = 9588921272.50566179874517327053929... = (c2^2 + 2*c0*c1)/3  if mod(n,3)=1

c = 9588921272.49785814355801212400055... = (c1^2 + 2*c0*c2)/3  if mod(n,3)=2

For the constants c0, c1, c2 see A006906.

(End)

G.f.: exp(2*Sum_{j>=1} Sum_{k>=1} k^j*x^(j*k)/j). - Ilya Gutkovskiy, Feb 07 2018

MATHEMATICA

nmax = 40; CoefficientList[Series[Product[1/(1-k*x^k)^2, {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Jan 06 2016 *)

PROG

(PARI)

N=66; q='q+O('q^N);

gf= 1/prod(n=1, N, (1-n*q^n)^2 );

Vec(gf)

/* Joerg Arndt, Oct 06 2012 */

(MAGMA) n:=40; R<x>:=PowerSeriesRing(Integers(), n); Coefficients(R!(&*[(1/(1-m*x^m))^2:m in [1..n]])); // G. C. Greubel, Jul 25 2018

CROSSREFS

Cf. A006906, A022662.

Column k=2 of A297328.

Sequence in context: A161870 A072338 A182197 * A192873 A017925 A030236

Adjacent sequences:  A022723 A022724 A022725 * A022727 A022728 A022729

KEYWORD

nonn

AUTHOR

N. J. A. Sloane

EXTENSIONS

Added more terms, Joerg Arndt, Oct 06 2012

STATUS

approved

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Last modified March 19 17:21 EDT 2019. Contains 321330 sequences. (Running on oeis4.)