A205811 G.f.: Product_{n>=1} [ (1 - x^n) / (1 - (n+1)^n*x^n) ]^(1/n).

1, 1, 6, 29, 221, 1897, 23502, 335334, 5923570, 119354491, 2758647259, 71079498533, 2031108928680, 63520842121792, 2161164726505952, 79394066773371245, 3133259427956392983, 132166451829847198316, 5934636812034634649249, 282609413111134846839482

Offset

0,3

Comments

Here sigma(n,k) equals the sum of the k-th powers of the divisors of n.

Links

Table of n, a(n) for n=0..19.

Formula

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

Example

G.f.: A(x) = 1 + x + 6*x^2 + 29*x^3 + 221*x^4 + 1897*x^5 + 23502*x^6 +...
where the g.f. equals the product:
A(x) = (1-x)/(1-2*x) * ((1-x^2)/(1-3^2*x^2))^(1/2) * ((1-x^3)/(1-4^3*x^3))^(1/3) * ((1-x^4)/(1-5^4*x^4))^(1/4) * ((1-x^5)/(1-6^5*x^5))^(1/5) *...
The logarithm equals the l.g.f. of A205812:
log(A(x)) = x + 11*x^2/2 + 70*x^3/3 + 719*x^4/4 + 7806*x^5/5 + 122534*x^6/6 +...

Prog

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

Crossrefs

Cf. A205812 (log), A205814, A023881.

Sequence in context: A294312 A054748 A209112 * A143563 A266205 A344434

Adjacent sequences: A205808 A205809 A205810 * A205812 A205813 A205814

Keyword

nonn

Author

Paul D. Hanna, Feb 01 2012

Status

approved