A198520 G.f. satisfies: A(x) = exp( Sum_{n>=1} A(x)^n / A(x^n) * x^n/n ).

1, 1, 1, 2, 4, 9, 22, 55, 141, 370, 986, 2662, 7264, 20006, 55534, 155219, 436456, 1233822, 3504482, 9996417, 28624038, 82248498, 237082689, 685375920, 1986604360, 5772399530, 16810591254, 49059068617, 143450142998, 420213814655, 1233034693847, 3623838769503

Offset

0,4

Links

Table of n, a(n) for n=0..31.

Example

G.f.: A(x) = 1 + x + x^2 + 2*x^3 + 4*x^4 + 9*x^5 + 22*x^6 + 55*x^7 +...
where
log(A(x)) = x +  A(x)^2/A(x^2)*x^2/2 + A(x)^3/A(x^3)*x^3/3 + A(x)^4/A(x^4)*x^4/4 +...
more explicitly,
log(A(x)) = x + x^2/2 + 4*x^3/3 + 9*x^4/4 + 26*x^5/5 + 76*x^6/6 + 218*x^7/7 +...

Prog

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

Crossrefs

Cf. A198413.

Sequence in context: A343291 A290996 A373245 * A115324 A196307 A107092

Adjacent sequences: A198517 A198518 A198519 * A198521 A198522 A198523

Keyword

nonn

Author

Paul D. Hanna, Oct 26 2011

Status

approved