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A285927
Expansion of (Product_{k>0} (1 - x^(3*k)) / (1 - x^k))^3 in powers of x.
5
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
Mohammed L. Nadji and Moussa Ahmia, Congruences for L-regular tripartitions for L in {2, 3}, Integers (2024) Vol. 24, Art. No. A86. See p. 2.
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).
Sequence in context: A145947 A373309 A153084 * A147371 A075188 A051894
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Apr 28 2017
STATUS
approved