A329157 Expansion of Product_{k>=1} (1 - Sum_{j>=1} j * x^(k*j)).

1, -1, -3, -3, -4, 3, 2, 19, 21, 32, 40, 45, 16, 8, -18, -125, -164, -291, -358, -530, -588, -724, -592, -675, -358, -207, 570, 1201, 2208, 3333, 4944, 6490, 8277, 10492, 11800, 13260, 14328, 14722, 12942, 12075, 5640, 603, -10444, -21120, -39360, -55876, -83488

Offset

0,3

Comments

Convolution inverse of A329156.

Links

Table of n, a(n) for n=0..46.

Formula

G.f.: Product_{k>=1} (1 - x^k / (1 - x^k)^2).

G.f.: exp(-Sum_{k>=1} ( Sum_{d|k} 1 / (d * (1 - x^(k/d))^(2*d)) ) * x^k).

G.f.: Product_{k>=1} (1 - x^k)^A032198(k).

G.f.: A(x) = Product_{k>=1} 1 / B(x^k), where B(x) = g.f. of A088305.

Mathematica

nmax = 46; CoefficientList[Series[Product[(1 - Sum[j x^(k j), {j, 1, nmax}]), {k, 1, nmax}], {x, 0, nmax}], x]
nmax = 46; CoefficientList[Series[Product[(1 - x^k/(1 - x^k)^2), {k, 1, nmax}], {x, 0, nmax}], x]

Crossrefs

Cf. A032198, A077285, A088305, A104575, A319668, A329156.

Sequence in context: A023647 A332413 A239207 * A082978 A005536 A172515

Adjacent sequences: A329154 A329155 A329156 * A329158 A329159 A329160

Keyword

sign

Author

Ilya Gutkovskiy, Nov 06 2019

Status

approved