A205502 G.f. satisfies: A(x) = exp( Sum_{n>=1} x^n/n * Product_{d|n} A(d*x^(n/d))^d ).

1, 1, 2, 6, 26, 153, 1230, 13364, 196940, 3964902, 110220876, 4272079445, 232593337728, 17882578732969, 1948605911230499, 301712214427188701, 66502429409739480660, 20895237675211683912974, 9368442364990639729658716, 5998494566458610304486161295

Offset

0,3

Links

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

Example

G.f.: A(x) = 1 + x + 2*x^2 + 6*x^3 + 26*x^4 + 153*x^5 + 1230*x^6 +...
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^2)^2*A(4*x)^4/4 + x^5*A(x^5)*A(5*x)^5/5 + x^6*A(x^6)*A(2*x^3)^2*A(3*x^2)^3*A(6*x)^6/6 +...
Explicitly,
log(A(x)) = x + 3*x^2/2 + 13*x^3/3 + 79*x^4/4 + 616*x^5/5 + 6297*x^6/6 + 83518*x^7/7 + 1454615*x^8/8 +...

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^d, x, d*x^(m/d) +x*O(x^n)))))))); polcoeff(A, n)}

Crossrefs

Cf. A205498, A205499, A205500, A205501.

Sequence in context: A003659 A159602 A032271 * A107104 A141761 A355206

Adjacent sequences: A205499 A205500 A205501 * A205503 A205504 A205505

Keyword

nonn

Author

Paul D. Hanna, Jan 27 2012

Status

approved