A309730 - OEIS

A309730

Expansion of Sum_{k>=1} x^k * (1 - x^(3*k))/(1 - x^k)^4.

1, 5, 11, 24, 32, 61, 65, 109, 120, 172, 167, 279, 236, 343, 358, 470, 410, 630, 515, 762, 706, 865, 761, 1193, 933, 1216, 1174, 1497, 1220, 1850, 1397, 1959, 1762, 2098, 1882, 2739, 2000, 2629, 2470, 3188, 2462, 3614, 2711, 3723, 3438, 3871, 3245, 4939, 3594, 4749, 4246, 5214

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OFFSET

1,2

COMMENTS

Inverse Moebius transform of centered triangular numbers (A005448).

LINKS

Table of n, a(n) for n=1..52.

FORMULA

G.f.: Sum_{k>=1} (3*k*(k - 1)/2 + 1) * x^k/(1 - x^k).

a(n) = 3 * (sigma_2(n) - sigma_1(n))/2 + d(n).

MATHEMATICA

nmax = 52; CoefficientList[Series[Sum[x^k (1 - x^(3 k))/(1 - x^k)^4, {k, 1, nmax}], {x, 0, nmax}], x] // Rest