A038064 Product_{k>=1} 1/(1 - x^k)^a(k) = 1 + 3x.

3, -6, 8, -18, 48, -124, 312, -810, 2184, -5928, 16104, -44220, 122640, -341796, 956576, -2690010, 7596480, -21524412, 61171656, -174336264, 498111952, -1426419852, 4093181688, -11767874940, 33891544368, -97764131640

Offset: 1

Author

Christian G. Bower, Jan 04 1999

Keywords

• sign

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..2000
• N. J. A. Sloane, Euler transform

Crossrefs

Cf. A038063, A038064, A038065, A038066, A038067, A038068, A038069, A038070.

Programs

PARI

{a(n)=polcoeff(sum(k=1,n,moebius(k)/k*log(1+3*x^k+x*O(x^n))),n)} \\ Paul D. Hanna, Oct 13 2010

Formula

G.f.: Sum_{n>=1} moebius(n)*log(1 + 3*x^n)/n, where moebius(n)=A008683(n). - Paul D. Hanna, Oct 13 2010

a(n) = -(1/n) * Sum_{d|n} mu(n/d) * (-3)^d. - Seiichi Manyama, Apr 12 2025