A281455 Expansion of Product_{k>=1} (1 + x^(7*k-2)).

1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 2, 0, 1, 0, 0, 1, 0, 2, 0, 1, 0, 0, 1, 0, 3, 0, 1, 0, 0, 2, 0, 3, 0, 1, 0, 0, 3, 0, 4, 0, 1, 1, 0, 4, 0, 4, 0, 1, 1, 0, 5, 0, 5, 0, 1, 2, 0, 7, 0, 5, 0, 1, 3, 0, 8, 0

Offset

0,32

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..10000

Formula

a(n) ~ exp(sqrt(n/21)*Pi) / (2^(12/7)*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 - 2)), {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] == 5, Do[poly[[j + 1]] += poly[[j - k + 1]], {j, nmax, k, -1}]; ], {k, 2, nmax}]; poly

Crossrefs

Cf. A109707, A281245, A281456, A281457, A281458, A280457.

Sequence in context: A071006 A227740 A284503 * A284500 A281458 A178781

Adjacent sequences: A281452 A281453 A281454 * A281456 A281457 A281458

Keyword

nonn

Author

Vaclav Kotesovec, Jan 22 2017

Status

approved