A192207 G.f. A(x) satisfies A(x) = 1 + Sum_{n>=1} A(x)^n*x^n/(1 - x^n).

1, 1, 3, 8, 25, 79, 268, 931, 3340, 12221, 45525, 171932, 657002, 2535167, 9864727, 38663036, 152491244, 604788048, 2410462518, 9649584165, 38782437824, 156428161276, 633003302363, 2569122403034, 10455470193615, 42656724160734

Offset

0,3

Links

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

Formula

G.f. satisfies: A(x) = 1 + Sum_{n>=1} x^n * Sum_{d|n} A(x)^d.

Example

G.f.: A(x) = 1 + x + 3*x^2 + 8*x^3 + 25*x^4 + 79*x^5 + 268*x^6 +...
which satisfies
A(x) = 1 + A(x)*x/(1-x) + A(x)^2*x^2/(1-x^2) + A(x)^3*x^3/(1-x^3) +...
The g.f. A = A(x) also satisfies
A = 1 + x*A + x^2*(A + A^2) + x^3*(A + A^3) + x^4*(A + A^2 + A^4) + x^5*(A + A^5) + x^6*(A + A^2 + A^3 + A^6) + x^7*(A + A^7) + x^8*(A + A^2 + A^4 + A^8) +...

Prog

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

Crossrefs

Sequence in context: A050383 A060404 A192905 * A289593 A101490 A148793

Adjacent sequences: A192204 A192205 A192206 * A192208 A192209 A192210

Keyword

nonn

Author

Paul D. Hanna, Jun 25 2011

Status

approved