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A285472
Expansion of Product_{k>=1} ((1 + x^(4*k)) / (1 - x^k)).
2
1, 1, 2, 3, 6, 8, 13, 18, 28, 38, 55, 74, 106, 140, 192, 253, 342, 444, 588, 758, 992, 1267, 1634, 2072, 2650, 3334, 4218, 5276, 6627, 8234, 10262, 12682, 15708, 19308, 23764, 29070, 35597, 43340, 52792, 64008, 77622, 93724, 113160, 136124, 163712, 196225
OFFSET
0,3
COMMENTS
a(n) is the number of overpartitions wherein only parts that are a multiple of four may be overlined. - Alois P. Heinz, Feb 03 2025
LINKS
FORMULA
a(n) ~ sqrt(3) * exp(sqrt(3*n)*Pi/2) / (16*n).
MAPLE
b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,
b(n, i-1)+`if`(irem(i, 4)=0, 2, 1)*add(b(n-i*j, i-1), j=1..n/i)))
end:
a:= n-> b(n$2):
seq(a(n), n=0..45); # Alois P. Heinz, Feb 03 2025
MATHEMATICA
nmax = 50; CoefficientList[Series[Product[((1+x^(4*k))/(1-x^k)), {k, 1, nmax}], {x, 0, nmax}], x]
CROSSREFS
KEYWORD
nonn
AUTHOR
Vaclav Kotesovec, Apr 19 2017
STATUS
approved