A262928 - OEIS

A262928

Expansion of Product_{k>=0} (1 + x^(3*k+2)).

1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 1, 0, 2, 1, 1, 2, 1, 1, 3, 1, 2, 3, 1, 3, 4, 2, 4, 4, 2, 5, 5, 3, 7, 5, 4, 8, 6, 6, 10, 7, 7, 12, 8, 10, 14, 9, 12, 16, 11, 16, 19, 13, 19, 21, 16, 24, 25, 19, 28, 28, 23, 35, 32, 28, 40, 36, 34, 48, 42, 41, 55, 47, 49, 65, 55

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

OFFSET

0,14

LINKS

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

FORMULA

a(n) ~ exp(sqrt(n)*Pi/3) / (2^(5/3)*sqrt(3)*n^(3/4)) * (1 - (Pi/144 + 9/(8*Pi)) / sqrt(n)). - Vaclav Kotesovec, Oct 04 2015, extended Jan 16 2017

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

MATHEMATICA

nmax=100; CoefficientList[Series[Product[(1+x^(3*k-1)), {k, 1, nmax}], {x, 0, nmax}], x]

nmax = 100; poly = ConstantArray[0, nmax + 1]; poly[[1]] = 1; poly[[2]] = 0; Do[If[Mod[k, 3] == 2, Do[poly[[j + 1]] += poly[[j - k + 1]], {j, nmax, k, -1}]; ], {k, 2, nmax}]; poly (* Vaclav Kotesovec, Jan 13 2017 *)

CROSSREFS

Cf. A003105, A035386, A261612.

Sequence in context: A078770 A072038 A284315 * A228429 A108316 A322426

Adjacent sequences: A262925 A262926 A262927 * A262929 A262930 A262931

KEYWORD

nonn

AUTHOR

Vaclav Kotesovec, Oct 04 2015

STATUS

approved