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A308291 Expansion of Sum_{k>=1} mu(k)*log(1 + x^k/(1 - x^k)^4)/k. 1
1, 3, 6, 4, -3, -22, -23, 8, 88, 139, -19, -472, -869, -101, 2684, 5668, 2104, -15300, -37680, -22428, 86645, 252383, 202936, -482512, -1694944, -1710607, 2584008, 11368664, 13819803, -12802724, -75911328, -108463344, 53647377, 503132556, 833364427, -127320060 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Inverse Euler transform of tetrahedral numbers (A000292).

LINKS

Table of n, a(n) for n=1..36.

FORMULA

-1 + Product_{n>=1} 1/(1 - x^n)^a(n) = g.f. of A000292.

MATHEMATICA

nmax = 36; CoefficientList[Series[Sum[MoebiusMu[k] Log[1 + x^k/(1 - x^k)^4]/k, {k, 1, nmax}], {x, 0, nmax}], x] // Rest

nmax = 50; s = ConstantArray[0, nmax]; Do[s[[j]] = j^2*(j + 1)*(j + 2)/6 - Sum[s[[d]]*(j - d)*(j - d + 1)*(j - d + 2)/6, {d, 1, j - 1}], {j, 1, nmax}]; Table[Sum[MoebiusMu[k/d]*s[[d]], {d, Divisors[k]}]/k, {k, 1, nmax}] (* Vaclav Kotesovec, Aug 10 2019 *)

CROSSREFS

Cf. A000292, A000335, A008683, A308290.

Sequence in context: A187148 A105559 A090038 * A006464 A233825 A159354

Adjacent sequences:  A308288 A308289 A308290 * A308292 A308293 A308294

KEYWORD

sign

AUTHOR

Ilya Gutkovskiy, May 18 2019

STATUS

approved

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Last modified January 19 21:47 EST 2020. Contains 331066 sequences. (Running on oeis4.)