A285927 Expansion of (Product_{k>0} (1 - x^(3*k)) / (1 - x^k))^3 in powers of x.

1, 3, 9, 19, 42, 81, 155, 276, 486, 821, 1368, 2214, 3541, 5544, 8586, 13082, 19740, 29403, 43414, 63423, 91935, 132075, 188418, 266733, 375232, 524331, 728514, 1006216, 1382604, 1889739, 2570719, 3480420, 4691682, 6297102, 8418252, 11209347, 14870970

Offset

0,2

Links

Seiichi Manyama, Table of n, a(n) for n = 0..10000

Formula

a(0) = 1, a(n) = (3/n)*Sum_{k=1..n} A046913(k)*a(n-k) for n > 0.

a(n) ~ exp(2*Pi*sqrt(n/3)) / (2 * 3^(7/4) * n^(3/4)). - Vaclav Kotesovec, Apr 30 2017

Mathematica

nmax = 40; CoefficientList[Series[Product[((1 - x^(3*k)) / (1 - x^k))^3, {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Apr 30 2017 *)

Crossrefs

(Product_{k>0} (1 - x^(m*k)) / (1 - x^k))^m: A022567 (m=2), this sequence (m=3), A093160 (m=4), A285928 (m=5).

Cf. A000726, A199659.

Sequence in context: A146662 A145947 A153084 * A147371 A075188 A051894

Adjacent sequences: A285924 A285925 A285926 * A285928 A285929 A285930

Keyword

nonn

Author

Seiichi Manyama, Apr 28 2017

Status

approved