A192497 G.f. satisfies: A(x) = 1 + Sum_{n>=1} x^n*A(x)^sigma(n), where sigma(n) = A000203(n) is the sum of divisors of n.

1, 1, 2, 6, 20, 73, 281, 1124, 4633, 19547, 84023, 366695, 1620513, 7237034, 32609389, 148066067, 676805101, 3111807931, 14381741533, 66775448718, 311332294182, 1456999560630, 6841841485578, 32228152992893, 152241706312812, 721055062770213

Offset

0,3

Links

Table of n, a(n) for n=0..25.

Example

G.f.: A(x) = 1 + x + 2*x^2 + 6*x^3 + 20*x^4 + 73*x^5 + 281*x^6 +...
The g.f. satisfies:
A(x) = 1 + x*A(x) + x^2*A(x)^3 + x^3*A(x)^4 + x^4*A(x)^7 + x^5*A(x)^6 + x^6*A(x)^12 + x^7*A(x)^8 + x^8*A(x)^15 +...

Prog

(PARI) {a(n)=local(A=1+x); for(i=1, n, A=1+sum(m=1, n, x^m*(A+x*O(x^n))^sigma(m))); polcoeff(A, n)}

Crossrefs

Sequence in context: A150140 A061396 A230823 * A104632 A194956 A150141

Adjacent sequences: A192494 A192495 A192496 * A192498 A192499 A192500

Keyword

nonn

Author

Paul D. Hanna, Jul 02 2011

Status

approved