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A293182 Expansion of Product_{k>=1} (1 + 2*x^k - x^(2*k)). 2
1, 2, 1, 6, 3, 6, 16, 12, 16, 22, 51, 36, 60, 62, 91, 154, 148, 176, 236, 278, 328, 552, 508, 670, 771, 988, 1068, 1438, 1844, 1998, 2401, 2882, 3300, 4030, 4640, 5406, 7212, 7584, 9072, 10480, 12612, 13964, 17024, 18860, 22545, 27298, 30340, 34372, 41068 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Robert Israel, Table of n, a(n) for n = 0..10000

FORMULA

a(n) ~ c^(1/4) * exp(2*sqrt(c*n)) / (2^(3/2) * sqrt(Pi) * n^(3/4)), where c = Pi^2/6 + log(1+sqrt(2))^2/2 + polylog(2, 3-2*sqrt(2))/2 - 2*polylog(2, sqrt(2)-1) = 1.18805291660775259061867850175092520191179528961165451864292...

MAPLE

N:= 100:

P:= mul(1+2*x^m- x^(2*m), m=1..N):

S:= series(P, x, N+1):

seq(coeff(S, x, n), n=0..N); # Robert Israel, Oct 01 2017

MATHEMATICA

nmax = 100; CoefficientList[Series[Product[1+2*x^k-x^(2*k), {k, 1, nmax}], {x, 0, nmax}], x]

CROSSREFS

Cf. A162891, A263401, A276527, A293138.

Sequence in context: A100014 A062566 A126265 * A124441 A284475 A285355

Adjacent sequences:  A293179 A293180 A293181 * A293183 A293184 A293185

KEYWORD

nonn

AUTHOR

Vaclav Kotesovec, Oct 01 2017

STATUS

approved

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Last modified October 21 16:14 EDT 2019. Contains 328302 sequences. (Running on oeis4.)