A156211 G.f.: A(x) = exp( Sum_{n>=1} 2^(n^2)*sigma(n)*x^n/n ), a power series in x with integer coefficients.

1, 2, 26, 732, 116390, 40513052, 137522735588, 643647384796344, 34588935490621449862, 3492521559898834682830380, 2281778066215315012669841569932, 2900138372618260977222563124493089544

Offset

0,2

Comments

Compare to g.f. of partition numbers: exp( Sum_{n>=1} sigma(n)*x^n/n ), where sigma(n) = A000203(n) is the sum of the divisors of n.

Links

Table of n, a(n) for n=0..11.

Example

G.f.: A(x) = 1 + 2*x + 26*x^2 + 732*x^3 + 116390*x^4 + 40513052*x^5 +...
log(A(x)) = 2*x + 2^4*3*x^2/2 + 2^9*4*x^3/3 + 2^16*7*x^4/4 + 2^25*6*x^5/5 +...

Prog

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

Crossrefs

Cf. A000041, A000203.

Sequence in context: A373869 A371297 A206601 * A156212 A138524 A329556

Adjacent sequences: A156208 A156209 A156210 * A156212 A156213 A156214

Keyword

nonn

Author

Paul D. Hanna, Feb 06 2009

Status

approved