A217334 G.f.: exp( Sum_{n>=1} (2*sigma(n^2) - sigma(n)^2 - sigma(n,2))/2 * x^n/n ).

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, -15, -11, -9, -29, -5, -56, -14, -56, -24, -101, 10, -140, -8, -25, 18, -101, 27, 7, 50, 91, 128, 222, 29, 300, 207, 516, 119, 614, 73, 762, 115, 510, 89, 614, -280

Offset

0,9

Comments

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

Links

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

Example

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 +...
where
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 +...

Prog

(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)}
for(n=0, 70, print1(a(n), ", "))

Crossrefs

Sequence in context: A059202 A244963 A144452 * A369455 A353859 A058865

Adjacent sequences: A217331 A217332 A217333 * A217335 A217336 A217337

Keyword

sign

Author

Paul D. Hanna, Sep 30 2012

Status

approved