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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
OFFSET
0,2
COMMENTS
Invert transform of A015128.
LINKS
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
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Oct 18 2018
STATUS
approved