A195734 - OEIS

%I #7 Mar 30 2012 18:37:29

%S 1,1,3,6,11,22,40,72,123,215,363,605,991,1618,2598,4139,6537,10229,

%T 15871,24476,37487,56995,86177,129531,193662,287992,426254,627841,

%U 920708,1344331,1954987,2831688,4086168,5875087,8417724,12020250,17108958,24275947,34340966

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

%H Paul D. Hanna, <a href="/A195734/b195734.txt">Table of n, a(n) for n = 0..1000</a>

%F Logarithmic derivative equals A195735.

%e G.f.: A(x) = 1 + x + 3*x^2 + 6*x^3 + 11*x^4 + 22*x^5 + 40*x^6 + 72*x^7 +...

%e where

%e log(A(x)) = x + 5*x^2/2 + 10*x^3/3 + 13*x^4/4 + 26*x^5/5 + 38*x^6/6 + 50*x^7/7 + 29*x^8/8 +...+ A195735(n)*x^n/n +...

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

%Y Cf. A195735 (log), A156302, A156303, A000203.

%K nonn

%O 0,3

%A _Paul D. Hanna_, Sep 22 2011