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A302018
Expansion of 1/(1 - x*(1 + theta_3(x))/2), where theta_3() is the Jacobi theta function.
2
1, 1, 2, 3, 5, 9, 15, 26, 44, 75, 129, 220, 377, 644, 1101, 1883, 3219, 5506, 9414, 16098, 27527, 47069, 80488, 137630, 235343, 402427, 688134, 1176685, 2012085, 3440591, 5883279, 10060183, 17202533, 29415676, 50299693, 86010564, 147074801, 251492331, 430042340, 735356089, 1257431006
OFFSET
0,3
FORMULA
G.f.: 1/(1 - x*Sum_{k>=0} x^(k^2)).
a(0) = 1; a(n) = Sum_{k=1..n} A010052(k-1)*a(n-k).
MATHEMATICA
nmax = 40; CoefficientList[Series[1/(1 - x (1 + EllipticTheta[3, 0, x])/2), {x, 0, nmax}], x]
nmax = 40; CoefficientList[Series[1/(1 - x Sum[x^k^2, {k, 0, nmax}]), {x, 0, nmax}], x]
CROSSREFS
Antidiagonal sums of A045847.
Sequence in context: A073031 A114138 A114140 * A096816 A220127 A286887
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Mar 30 2018
STATUS
approved