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A320942 Expansion of Sum_{k>=1} (-1 + Product_{j>=1} (1 + x^(k*j))/(1 - x^(k*j))). 0
2, 6, 10, 20, 26, 54, 66, 120, 164, 262, 346, 572, 730, 1110, 1506, 2182, 2866, 4156, 5402, 7612, 9978, 13638, 17730, 24200, 31092, 41558, 53572, 70692, 90250, 118406, 150146, 194794, 246610, 316678, 398730, 509560, 637594, 808342, 1009186, 1270984, 1578530, 1978758, 2447066 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Inverse Möbius transform of A015128.

LINKS

Table of n, a(n) for n=1..43.

N. J. A. Sloane, Transforms

FORMULA

G.f.: Sum_{k>=1} A015128(k)*x^k/(1 - x^k).

G.f.: Sum_{k>=1} (1/theta_4(x^k) - 1), where theta_4() is the Jacobi theta function.

a(n) = Sum_{d|n} A015128(d).

MAPLE

a:=series(add(-1+mul((1+x^(k*j))/(1-x^(k*j)), j=1..100), k=1..100), x=0, 44): seq(coeff(a, x, n), n=1..43); # Paolo P. Lava, Apr 02 2019

MATHEMATICA

nmax = 43; Rest[CoefficientList[Series[Sum[-1 + Product[(1 + x^(k j))/(1 - x^(k j)), {j, 1, nmax}], {k, 1, nmax}], {x, 0, nmax}], x]]

nmax = 43; Rest[CoefficientList[Series[Sum[1/EllipticTheta[4, 0, x^k] - 1, {k, 1, nmax}], {x, 0, nmax}], x]]

Table[Sum[Sum[PartitionsP[d - k] PartitionsQ[k], {k, 0, d}], {d, Divisors[n]}], {n, 43}]

CROSSREFS

Cf. A015128, A047966, A047968, A300274.

Sequence in context: A077084 A239542 A007926 * A168152 A211982 A096338

Adjacent sequences:  A320939 A320940 A320941 * A320943 A320944 A320945

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Oct 24 2018

STATUS

approved

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Last modified April 17 22:48 EDT 2021. Contains 343071 sequences. (Running on oeis4.)