A198944 G.f.: A(x) = exp( Sum_{n>=1} [Sum_{k=0..n} C(n,k)^3 * x^k*A(x)^k] * x^n/n ).

1, 1, 2, 7, 23, 78, 291, 1126, 4436, 17910, 73773, 308188, 1303402, 5573133, 24050795, 104620985, 458324429, 2020417339, 8956142180, 39899217350, 178549985024, 802275736073, 3618237414959, 16373514195570, 74325340129430, 338356926399193, 1544406450870590

Offset: 0

Author

Paul D. Hanna, Oct 31 2011

Keywords

• nonn

Comments

Compare to a g.f. G(x) of A036765 (rooted trees with a degree constraint):

G(x) = exp( Sum_{n>=1} [Sum_{k=0..n} C(n,k)^2 * x^k*G(x)^k] * x^n/n ).

Examples

			G.f.: A(x) = 1 + x + 2*x^2 + 7*x^3 + 23*x^4 + 78*x^5 + 291*x^6 +...
where
log(A(x)) = (1 + x*A(x))*x + (1 + 2^3*x*A(x) + x^2*A(x)^2)*x^2/2 +
(1 + 3^3*x*A(x) + 3^3*x^2*A(x)^2 + x^3*A(x)^3)*x^3/3 +
(1 + 4^3*x*A(x) + 6^3*x^2*A(x)^2 + 4^3*x^3*A(x)^3 + x^4*A(x)^4)*x^4/4 +
(1 + 5^3*x*A(x) + 10^3*x^2*A(x)^2 + 10^3*x^3*A(x)^3 + 5^3*x^4*A(x)^4 + x^5*A(x)^5)*x^5/5 +...
more explicitly,
log(A(x)) = x + 3*x^2/2 + 16*x^3/3 + 63*x^4/4 + 251*x^5/5 + 1110*x^6/6 +...
		

Crossrefs

Cf. A036765, A192131.

Programs

PARI

{a(n)=local(A=1+x); for(i=1, n, A=exp(sum(m=1, n, sum(j=0, m, binomial(m, j)^3*(x*A+x*O(x^n))^j)*x^m/m))); polcoeff(A, n, x)}