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A281243 Expansion of Product_{k>=1} (1 + x^(5*k-1)). 16
1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 0, 2, 1, 0, 0, 1, 2, 1, 0, 0, 1, 3, 1, 0, 0, 2, 3, 1, 0, 0, 3, 4, 1, 0, 1, 4, 4, 1, 0, 1, 5, 5, 1, 0, 2, 7, 5, 1, 0, 3, 8, 6, 1, 0, 5, 10, 6, 1, 1, 6, 12, 7, 1, 1, 9, 14, 7, 1, 2, 11, 16, 8, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,24

COMMENTS

Convolution of this sequence and A280454 is A203776.

LINKS

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

FORMULA

a(n) ~ exp(sqrt(n/15)*Pi) / (2^(9/5)*15^(1/4)*n^(3/4)) * (1 + (Pi/(240*sqrt(15)) - 3*sqrt(15)/(8*Pi)) / sqrt(n)). - Vaclav Kotesovec, Jan 18 2017, extended Jan 24 2017

MATHEMATICA

nmax = 200; CoefficientList[Series[Product[(1 + x^(5*k - 1)), {k, 1, nmax}], {x, 0, nmax}], x]

nmax = 200; poly = ConstantArray[0, nmax + 1]; poly[[1]] = 1; poly[[2]] = 0; Do[If[Mod[k, 5] == 4, Do[poly[[j + 1]] += poly[[j - k + 1]], {j, nmax, k, -1}]; ], {k, 2, nmax}]; poly

CROSSREFS

Cf. A262928, A147599, A281244, A281245.

Cf. A261612, A169975, A280454, A280456, A280457.

Sequence in context: A164118 A180981 A284317 * A284314 A280454 A124645

Adjacent sequences:  A281240 A281241 A281242 * A281244 A281245 A281246

KEYWORD

nonn

AUTHOR

Vaclav Kotesovec, Jan 18 2017

STATUS

approved

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Last modified August 22 02:44 EDT 2019. Contains 326169 sequences. (Running on oeis4.)