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.

1, 1, 3, 7, 16, 30, 64, 120, 236, 434, 805, 1445, 2614, 4568, 8003, 13783, 23616, 39886, 67124, 111652, 184862, 303282, 495001, 801939, 1292968, 2070628, 3300796, 5232112, 8256081, 12961543, 20264168, 31535316, 48882592, 75455902, 116041910, 177775284, 271401683

Offset: 0

Author

Paul D. Hanna, Apr 03 2013

Keywords

• nonn

Comments

Compare to: exp(-Sum_{n>=1} A113184(n)*x^n/n ) = Sum_{n>=1} (-x)^(n*(n+1)/2).

Examples

			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 +...
where
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 +...
		

Links

• Paul D. Hanna, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A224339, A113184.

Programs

PARI

{a(n)=polcoeff(exp(sum(k=1,n,sumdiv(k^2, d, (-1)^d*d)*(-x)^k/k)+x*O(x^n)),n)}
for(n=0,40,print1(a(n),", "))

Formula

Logarithmic derivative yields A224339.