A199103 G.f. satisfies: A(x) = exp( Sum_{n>=1} (1+x)^n * A(x^n) * x^n/n ).

1, 1, 3, 8, 23, 67, 202, 622, 1955, 6248, 20261, 66484, 220429, 737260, 2484734, 8429714, 28766001, 98670291, 340011308, 1176505537, 4086143638, 14239716570, 49776772808, 174492148048, 613266137776, 2160518118345, 7628244051977, 26988540797766, 95666557041459

Offset

0,3

Links

Table of n, a(n) for n=0..28.

Example

G.f.: A(x) = 1 + x + 3*x^2 + 8*x^3 + 23*x^4 + 67*x^5 + 202*x^6 + 622*x^7 +...
where
log(A(x)) = (1+x)*A(x)*x + (1+x)^2*A(x^2)*x^2/2 + (1+x)^3*A(x^3)*x^3/3 +...

Prog

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

Crossrefs

Cf. A199104.

Sequence in context: A025578 A038151 A230122 * A057198 A025262 A056010

Adjacent sequences: A199100 A199101 A199102 * A199104 A199105 A199106

Keyword

nonn

Author

Paul D. Hanna, Nov 03 2011

Status

approved