A281456 - OEIS

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A281456

Expansion of Product_{k>=1} (1 + x^(7*k-3)).

1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 2, 0, 0, 1, 1, 0, 0, 2, 0, 0, 1, 1, 0, 0, 3, 0, 0, 1, 2, 0, 0, 3, 0, 0, 1, 3, 0, 0, 4, 1, 0, 1, 4, 0, 0, 4, 1, 0, 1, 5, 0, 0, 5, 2, 0, 1, 7, 0, 0, 5, 3, 0, 1, 8, 0, 0, 6, 5

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,30

LINKS

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

FORMULA

a(n) ~ exp(sqrt(n/21)*Pi) / (2^(11/7)*21^(1/4)*n^(3/4)) * (1 - (3*sqrt(21)/(8*Pi) + 23*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 - 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, 7] == 4, Do[poly[[j + 1]] += poly[[j - k + 1]], {j, nmax, k, -1}]; ], {k, 2, nmax}]; poly

CROSSREFS

Cf. A109706, A281245, A281455, A281457, A281458, A280457.

Sequence in context: A258590 A057558 A284502 * A284501 A281457 A159708

Adjacent sequences: A281453 A281454 A281455 * A281457 A281458 A281459

KEYWORD

nonn

AUTHOR

Vaclav Kotesovec, Jan 22 2017

STATUS

approved