cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

This page as a plain text file.
%I A038064 #25 Apr 12 2025 09:37:16
%S A038064 3,-6,8,-18,48,-124,312,-810,2184,-5928,16104,-44220,122640,-341796,
%T A038064 956576,-2690010,7596480,-21524412,61171656,-174336264,498111952,
%U A038064 -1426419852,4093181688,-11767874940,33891544368,-97764131640
%N A038064 Product_{k>=1} 1/(1 - x^k)^a(k) = 1 + 3x.
%H A038064 Seiichi Manyama, <a href="/A038064/b038064.txt">Table of n, a(n) for n = 1..2000</a>
%H A038064 N. J. A. Sloane, <a href="/transforms.txt">Euler transform</a>
%F A038064 G.f.: Sum_{n>=1} moebius(n)*log(1 + 3*x^n)/n, where moebius(n)=A008683(n). - _Paul D. Hanna_, Oct 13 2010
%F A038064 a(n) = -(1/n) * Sum_{d|n} mu(n/d) * (-3)^d. - _Seiichi Manyama_, Apr 12 2025
%o A038064 (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
%Y A038064 Cf. A038063, A038064, A038065, A038066, A038067, A038068, A038069, A038070.
%K A038064 sign
%O A038064 1,1
%A A038064 _Christian G. Bower_, Jan 04 1999