A225957 O.g.f.: exp( Sum_{n>=1} -(sigma(2*n^3) - sigma(n^3)) * (-x)^n/n ).

1, 2, -6, 12, 38, -108, 148, 168, -922, 2294, -2656, -1732, 17908, -44516, 60896, -6936, -206474, 650848, -1181394, 1146324, 865832, -6609592, 16632596, -26643544, 22498916, 23275482, -144152248, 349896736, -563311472, 532552508, 233516176, -2378435472, 6264582710

Offset

0,2

Comments

Compare to the Jacobi theta_3 function:

1 + 2*Sum_{n>=1} x^(n^2) = exp( Sum_{n>=1} -(sigma(2*n) - sigma(n))*(-x)^n/n ).

Here sigma(n) = A000203(n), the sum of the divisors of n.

Links

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

Formula

O.g.f.: exp( Sum_{n>=1} -A054785(n^3)*(-x)^n/n ).

Example

O.g.f.: A(x) = 1 + 2*x - 6*x^2 + 12*x^3 + 38*x^4 - 108*x^5 + 148*x^6 + 168*x^7 +...
where
log(A(x)) = 2*x - 8*x^2/2 + 26*x^3/3 - 32*x^4/4 + 62*x^5/5 - 104*x^6/6 + 114*x^7/7 - 128*x^8/8 + 242*x^9/9 - 248*x^10/10 + 266*x^11/11 - 416*x^12/12 +...+ -(-1)^n*A054785(n^3)*x^n/n +...

Prog

(PARI) {a(n)=polcoeff(exp(sum(m=1, n, -(sigma(2*m^3)-sigma(m^3))*(-x)^m/m)+x^2*O(x^n)), n)}
for(n=0, 50, print1(a(n), ", "))

Crossrefs

Cf. A225958, A225959, A054785, A000203; variants: A215603, A225925, A195584.

Sequence in context: A189565 A074442 A162589 * A123045 A280171 A327879

Adjacent sequences: A225954 A225955 A225956 * A225958 A225959 A225960

Keyword

sign

Author

Paul D. Hanna, May 21 2013

Status

approved