A217334 - OEIS

%I #6 Sep 30 2012 22:05:43

%S 1,0,0,0,-1,0,-1,0,-3,-1,0,0,-4,1,3,0,4,3,1,1,16,4,10,0,15,-4,6,0,14,

%T -15,-11,-9,-29,-5,-56,-14,-56,-24,-101,10,-140,-8,-25,18,-101,27,7,

%U 50,91,128,222,29,300,207,516,119,614,73,762,115,510,89,614,-280

%N G.f.: exp( Sum_{n>=1} (2*sigma(n^2) - sigma(n)^2 - sigma(n,2))/2 * x^n/n ).

%C The number of contiguous signs appear to increase (roughly) in proportion to the square-root of the number of terms.

%H Paul D. Hanna, <a href="/A217334/b217334.txt">Table of n, a(n) for n = 0..1000</a>

%e G.f.: A(x) = 1 - x^4 - x^6 - 3*x^8 - x^9 - 4*x^12 + x^13 + 3*x^14 + 4*x^16 +...

%e where

%e log(A(x)) = -4*x^4/4 - 6*x^6/6 - 28*x^8/8 - 9*x^9/9 - 10*x^10/10 - 94*x^12/12 - 14*x^14/14 - 15*x^15/15 - 140*x^16/16 +...

%o (PARI) {a(n)=polcoeff(exp(sum(m=1,n,(sigma(m^2)-sigma(m)^2/2-sigma(m,2)/2)*x^m/m)+x*O(x^n)),n)}

%o for(n=0,70,print1(a(n),", "))

%K sign

%O 0,9

%A _Paul D. Hanna_, Sep 30 2012