A281272 Expansion of Product_{k>=1} (1 + x^(5*k-3)).

1, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 2, 0, 1, 1, 0, 2, 0, 1, 1, 0, 3, 0, 2, 1, 0, 3, 0, 3, 1, 1, 4, 0, 4, 1, 1, 4, 0, 5, 1, 2, 5, 0, 7, 1, 3, 5, 0, 8, 1, 5, 6, 1, 10, 1, 6, 6, 1, 12, 1, 9, 7, 2, 14, 1, 11, 7, 3, 16, 1, 15, 8, 5, 19, 1, 18

Offset

0,20

Links

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

Formula

a(n) ~ exp(sqrt(n/15)*Pi) / (2^(7/5)*15^(1/4)*n^(3/4)) * (1 - (3*sqrt(15)/(8*Pi) + 11*Pi/(240*sqrt(15))) / sqrt(n)). - Vaclav Kotesovec, Jan 18 2017, extended Jan 24 2017

Mathematica

nmax = 100; CoefficientList[Series[Product[(1 + x^(5*k - 3)), {k, 1, nmax}], {x, 0, nmax}], x]
nmax = 100; poly = ConstantArray[0, nmax + 1]; poly[[1]] = 1; poly[[2]] = 0; Do[If[Mod[k, 5] == 2, Do[poly[[j + 1]] += poly[[j - k + 1]], {j, nmax, k, -1}]; ], {k, 2, nmax}]; poly

Crossrefs

Cf. A219607, A281243, A281271, A280454.

Sequence in context: A284320 A281271 A284319 * A147310 A025886 A117355

Adjacent sequences: A281269 A281270 A281271 * A281273 A281274 A281275

Keyword

nonn

Author

Vaclav Kotesovec, Jan 18 2017

Status

approved