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A281458
Expansion of Product_{k>=1} (1 + x^(7*k-5)).
8
1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 2, 0, 1, 0, 0, 1, 0, 2, 0, 1, 0, 0, 1, 0, 3, 0, 2, 0, 0, 1, 0, 3, 0, 3, 0, 1, 1, 0, 4, 0, 4, 0, 1, 1, 0, 4, 0, 5, 0, 2, 1, 0, 5, 0, 7, 0, 3, 1, 0, 5, 0, 8, 0, 5, 1, 1, 6, 0, 10, 0, 6
OFFSET
0,26
LINKS
FORMULA
a(n) ~ exp(sqrt(n/21)*Pi) / (2^(9/7)*21^(1/4)*n^(3/4)) * (1 - (3*sqrt(21)/(8*Pi) + 11*Pi/(336*sqrt(21))) / sqrt(n)). - Vaclav Kotesovec, Jan 22 2017, extended Jan 24 2017
MATHEMATICA
nmax = 100; CoefficientList[Series[Product[(1 + x^(7*k - 5)), {k, 1, nmax}], {x, 0, nmax}], x]
nmax = 100; poly = ConstantArray[0, nmax + 1]; poly[[1]] = 1; poly[[2]] = 0; Do[If[Mod[k, 7] == 2, Do[poly[[j + 1]] += poly[[j - k + 1]], {j, nmax, k, -1}]; ], {k, 2, nmax}]; poly
CROSSREFS
KEYWORD
nonn
AUTHOR
Vaclav Kotesovec, Jan 22 2017
STATUS
approved