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A261615
Expansion of Product_{k>=0} (1 + x^(3*k+1))^2.
5
1, 2, 1, 0, 2, 4, 2, 2, 5, 4, 3, 8, 10, 6, 9, 14, 11, 14, 22, 18, 17, 30, 32, 28, 41, 46, 39, 54, 68, 60, 73, 94, 85, 96, 131, 128, 130, 170, 175, 176, 229, 246, 237, 294, 330, 320, 386, 446, 430, 492, 582, 578, 642, 762, 763, 818, 977, 1008, 1061, 1254, 1311
OFFSET
0,2
COMMENTS
Self-convolution of A261612.
In general, if a > 0, b > 0, GCD(a,b) = 1 and g.f. = Product_{k>=0} (1 + x^(a*k+b))^2, then a(n) ~ exp(Pi*sqrt(2*n/(3*a))) / (2^(2*b/a + 1/4) * 3^(1/4) * a^(1/4) * n^(3/4)).
FORMULA
a(n) ~ exp(Pi*sqrt(2*n)/3) / (2^(11/12) * sqrt(3) * n^(3/4)).
MATHEMATICA
nmax = 60; CoefficientList[Series[Product[(1 + x^(3*k+1))^2, {k, 0, nmax}], {x, 0, nmax}], x]
CROSSREFS
KEYWORD
nonn
AUTHOR
Vaclav Kotesovec, Aug 26 2015
STATUS
approved