A187736 G.f. satisfies: A(x) = x*Sum{n>=0} A( n*x/(1+n*x) )^n.

1, 1, 4, 30, 372, 6865, 180337, 6664746, 347126163, 25621940636, 2692407417070, 403782925417406, 86521373592454354, 26501533097131820625, 11604995872798575186212, 7265288737454158428096319, 6503007077048714757847413184, 8322734168520894445448609153627

Offset

1,3

Comments

Compare g.f. to the identity (cf. A001710):

Sum_{n>=0} ( n*x/(1+n*x) )^n = 1 + Sum_{n>=1} (n+1)!/2 * x^n.

Also compare to the identity:

G(x) = x*Sum_{n>=0} G( x/(1+x) )^n is satisfied by: G(x) = x/(1-x).

Links

Table of n, a(n) for n=1..18.

Example

G.f.: A(x) = x + x^2 + 4*x^3 + 30*x^4 + 372*x^5 + 6865*x^6 +...
where
A(x) = x + x*A(x/(1+x)) + x*A(2*x/(1+2*x))^2 + x*A(3*x/(1+3*x))^3 + x*A(4*x/(1+4*x))^4 + x*A(5*x/(1+5*x))^5 +...

Prog

(PARI) {a(n)=local(A=x); for(i=1, n, A=x*sum(m=0, n, subst(A, x, m*x/(1+m*x+x*O(x^n)))^m)); polcoeff(A, n)}
for(n=0, 20, print1(a(n), ", "))

Crossrefs

Sequence in context: A166892 A336712 A185523 * A199569 A363911 A326205

Adjacent sequences: A187733 A187734 A187735 * A187737 A187738 A187739

Keyword

nonn

Author

Paul D. Hanna, Jan 02 2013

Status

approved