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A320654 Expansion of 1/(2 - Product_{k>=1} (1 + x^k)/(1 - x^k)). 1
1, 2, 8, 32, 126, 496, 1952, 7680, 30216, 118882, 467728, 1840224, 7240160, 28485616, 112073536, 440941056, 1734834302, 6825515600, 26854243752, 105655081568, 415688349456, 1635480294080, 6434618135968, 25316300481024, 99604212169632, 391881866363890, 1541816293103184 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Invert transform of A015128.

LINKS

Table of n, a(n) for n=0..26.

N. J. A. Sloane, Transforms

FORMULA

G.f.: 1/(2 - 1/theta_4(x)), where theta_() is the Jacobi theta function.

a(0) = 1; a(n) = Sum_{k=1..n} A015128(k)*a(n-k).

MAPLE

a:=series(1/(2-mul((1+x^k)/(1-x^k), k=1..100)), x=0, 27): seq(coeff(a, x, n), n=0..26); # Paolo P. Lava, Apr 02 2019

MATHEMATICA

nmax = 26; CoefficientList[Series[1/(2 - Product[(1 + x^k)/(1 - x^k), {k, 1, nmax}]), {x, 0, nmax}], x]

nmax = 26; CoefficientList[Series[1/(2 - 1/EllipticTheta[4, 0, x]), {x, 0, nmax}], x]

a[0] = 1; a[n_] := a[n] = Sum[Sum[PartitionsP[k - j] PartitionsQ[j], {j, 0, k}] a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 26}]

CROSSREFS

Cf. A002448, A015128, A055887, A299108, A304969.

Sequence in context: A217665 A337863 A324568 * A333579 A274524 A081294

Adjacent sequences:  A320651 A320652 A320653 * A320655 A320656 A320657

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Oct 18 2018

STATUS

approved

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Last modified August 5 16:39 EDT 2021. Contains 346485 sequences. (Running on oeis4.)