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A292547
Number of partitions of n into distinct odd cubes.
4
1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0
OFFSET
0
COMMENTS
In general, if m > 0 and g.f. = Product_{k>=1} (1 + x^((2*k-1)^m)), then a(n) ~ exp((m+1) * ((2^(1/m)-1) * Gamma(1/m) * Zeta(1+1/m) / m^2)^(m/(m+1)) * n^(1/(m+1)) / 2) * ((2^(1/m)-1) * Gamma(1/m) * Zeta(1+1/m))^(m/(2*(m+1))) / (2*sqrt(Pi*(m+1)) * m^((m-1)/(2*(m+1))) * n^((2*m+1)/(2*(m+1)))).
LINKS
FORMULA
G.f.: Product_{k>=1} (1 + x^((2*k-1)^3)).
a(n) ~ exp(2 * 3^(-3/2) * ((2^(1/3)-1) * Gamma(1/3) * Zeta(4/3))^(3/4) * n^(1/4)) * ((2^(1/3)-1) * Gamma(1/3) * Zeta(4/3))^(3/8) / (4*3^(1/4) * sqrt(Pi) * n^(7/8)).
MATHEMATICA
nmax = 200; CoefficientList[Series[Product[1 + x^((2*k-1)^3), {k, 1, Floor[nmax^(1/3)/2] + 1}], {x, 0, nmax}], x]
CROSSREFS
Cf. A000700 (m=1), A167700 (m=2).
Sequence in context: A014071 A014038 A014067 * A014032 A014055 A256433
KEYWORD
nonn
AUTHOR
Vaclav Kotesovec, Sep 18 2017
STATUS
approved