A285443 Expansion of Product_{k>0} ((1-x^{5k-2}) * (1-x^{5k-3})/((1-x^{5k-1}) * (1-x^{5k-4})))^3 in powers of x.

1, 3, 3, -2, -6, 0, 12, 9, -15, -28, 3, 48, 33, -48, -87, 7, 135, 90, -134, -234, 21, 356, 237, -330, -575, 42, 831, 540, -762, -1296, 107, 1848, 1191, -1633, -2769, 210, 3842, 2448, -3366, -5634, 444, 7722, 4889, -6624, -11028, 840, 14871, 9342, -12636, -20877

Offset: 0

Author

Seiichi Manyama, Apr 19 2017

Keywords

• sign

Links

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

Crossrefs

Prod_{k>0} ((1-x^{5k-1}) * (1-x^{5k-4})/((1-x^{5k-2}) * (1-x^{5k-3})))^m: A285444 (m=-4), this sequence (m=-3), A285442 (m=-2), A003823 (m=-1), A007325 (m=1), A055101 (m=2), A055102 (m=3), A055103 (m=4).

Cf. A109091, A340455, A340456.

Formula

a(0) = 1, a(n) = (3/n)*Sum_{k=1..n} A109091(k)*a(n-k) for n > 0.

Expansion of cube of continued fraction 1 + x/(1 + x^2/(1 + x^3/(1 + x^4/(1 + ...)))). - Ilya Gutkovskiy, Apr 19 2017

G.f.: ( Sum_{k in Z} x^k / (1 - x^(5*k+1)) ) / ( Sum_{k in Z} x^(2*k) / (1 - x^(5*k+2)) ). - Seiichi Manyama, Jul 29 2024