A281243 - OEIS

The OEIS is supported by the many generous donors to the OEIS Foundation.

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give

A281243

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

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

G.f.: Sum_{k>=0} x^(k*(5*k + 3)/2) / Product_{j=1..k} (1 - x^(5*j)). - Ilya Gutkovskiy, Nov 24 2020

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