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

0,3

Comments

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

Links

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

Formula

Logarithmic derivative yields A224339.

Example

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 +...

Prog

(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), ", "))

Crossrefs

Cf. A224339, A113184.

Sequence in context: A213180 A110585 A184677 * A240739 A301117 A000412

Adjacent sequences: A224337 A224338 A224339 * A224341 A224342 A224343

Keyword

nonn

Author

Paul D. Hanna, Apr 03 2013

Status

approved