A205499 G.f. satisfies: A(x) = exp( Sum_{n>=1} x^n/n * Product_{d|n} A(d*x^n) ).

1, 1, 2, 4, 10, 22, 59, 140, 375, 948, 2568, 6670, 18305, 48755, 134666, 365881, 1017559, 2801369, 7848220, 21842497, 61530519, 172772037, 489296057, 1383418713, 3936301710, 11194022584, 31983684187, 91397174511, 262107839548, 752077861258, 2163980884425

Offset

0,3

Links

Table of n, a(n) for n=0..30.

Example

G.f.: A(x) = 1 + x + 2*x^2 + 4*x^3 + 10*x^4 + 22*x^5 + 59*x^6 + 140*x^7 +...
By definition:
log(A(x)) = x*A(x) + x^2*A(x^2)*A(2*x^2)/2 + x^3*A(x^3)*A(3*x^3)/3 + x^4*A(x^4)*A(2*x^4)*A(4*x^4)/4 + x^5*A(x^5)*A(5*x^5)/5 + x^6*A(x^6)*A(2*x^6)*A(3*x^6)*A(6*x^6)/6 +...
Explicitly,
log(A(x)) = x + 3*x^2/2 + 7*x^3/3 + 23*x^4/4 + 51*x^5/5 + 177*x^6/6 + 414*x^7/7 + 1327*x^8/8 + 3445*x^9/9 +...

Prog

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

Crossrefs

Cf. A205498, A205500, A205501, A205502.

Sequence in context: A205490 A221839 A354423 * A148086 A005962 A208062

Adjacent sequences: A205496 A205497 A205498 * A205500 A205501 A205502

Keyword

nonn

Author

Paul D. Hanna, Jan 27 2012

Status

approved