cp's OEIS Frontend

A224340 G.f.: exp( Sum_{n>=1} A113184(n^2)*x^n/n ), where A113184(n) = difference between sum of odd divisors of n and sum of even divisors of n.

%I A224340 #7 Apr 15 2013 21:24:42
%S A224340 1,1,3,7,16,30,64,120,236,434,805,1445,2614,4568,8003,13783,23616,
%T A224340 39886,67124,111652,184862,303282,495001,801939,1292968,2070628,
%U A224340 3300796,5232112,8256081,12961543,20264168,31535316,48882592,75455902,116041910,177775284,271401683
%N A224340 G.f.: exp( Sum_{n>=1} A113184(n^2)*x^n/n ), where A113184(n) = difference between sum of odd divisors of n and sum of even divisors of n.
%C A224340 Compare to: exp(-Sum_{n>=1} A113184(n)*x^n/n ) = Sum_{n>=1} (-x)^(n*(n+1)/2).
%H A224340 Paul D. Hanna, <a href="/A224340/b224340.txt">Table of n, a(n) for n = 0..1000</a>
%F A224340 Logarithmic derivative yields A224339.
%e A224340 L.g.f.: A(x) = 1 + x + 3*x^2 + 7*x^3 + 16*x^4 + 30*x^5 + 64*x^6 + 120*x^7 +...
%e A224340 where
%e A224340 log(A(x)) = x + 5*x^2/2 + 13*x^3/3 + 29*x^4/4 + 31*x^5/5 + 65*x^6/6 + 57*x^7/7 + 125*x^8/8 + 121*x^9/9 +...+ A113184(n^2)*x^n/n +...
%o A224340 (PARI) {a(n)=polcoeff(exp(sum(k=1,n,sumdiv(k^2, d, (-1)^d*d)*(-x)^k/k)+x*O(x^n)),n)}
%o A224340 for(n=0,40,print1(a(n),", "))
%Y A224340 Cf. A224339, A113184.
%K A224340 nonn
%O A224340 0,3
%A A224340 _Paul D. Hanna_, Apr 03 2013