A180608 O.g.f.: exp( Sum_{n>=1} A067692(n)*x^n/n ), where A067692(n) = [sigma(n)^2 + sigma(n,2)]/2.

1, 1, 4, 8, 21, 39, 93, 171, 364, 675, 1338, 2433, 4641, 8282, 15222, 26811, 47920, 83046, 145288, 248164, 425970, 718303, 1213106, 2020540, 3365352, 5541996, 9115640, 14856657, 24164430, 39002462, 62800603, 100454208, 160257140

Offset

0,3

Comments

sigma(n) = A000203(n), sum of divisors of n;

sigma(n,2) = A001157(n), sum of squares of divisors of n.

Links

Table of n, a(n) for n=0..32.

Example

O.g.f.: A(x) = 1 + x + 4*x^2 + 8*x^3 + 21*x^4 + 39*x^5 + 93*x^6 +...
log(A(x)) = x + 7*x^2/2 + 13*x^3/3 + 35*x^4/4 + 31*x^5/5 + 97*x^6/6 +...

Prog

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

Crossrefs

Cf. A067692, A000203, A001157.

Sequence in context: A006908 A079860 A061256 * A244583 A261031 A077921

Adjacent sequences: A180605 A180606 A180607 * A180609 A180610 A180611

Keyword

nonn

Author

Paul D. Hanna, Oct 10 2010

Status

approved