A224786 G.f. satisfies: A(x) = Sum_{n>=0} x^n / (A(x) - n*x)^n.

1, 1, 1, 2, 6, 23, 110, 607, 3742, 25324, 185566, 1457998, 12195992, 108010446, 1008224881, 9883048933, 101418491070, 1086613660608, 12126900841444, 140682966122152, 1693340044490513, 21111988598271746, 272228110567491910, 3625334790162237116

Offset

0,4

Links

Table of n, a(n) for n=0..23.

Formula

G.f. satisfies: A(x) = 1 + G(x/A(x)) where G(x) is the g.f. of A080108, where A080108(n) = Sum_{k=1..n} k^(n-k)*C(n-1,k-1).

Example

G.f.: A(x) = 1 + x + x^2 + 2*x^3 + 6*x^4 + 23*x^5 + 110*x^6 + 607*x^7 +...
where, by definition,
A(x) = 1 + x/(A(x) - x) + x^2/(A(x) - 2*x)^2 + x^3/(A(x) - 3*x)^3 + x^4/(A(x) - 4*x)^4 + x^5/(A(x) - 5*x)^5 +....
Also, the g.f. satisfies:
A(x) = 1 + x/A(x) + 2*x^2/A(x)^2 + 6*x^3/A(x)^3 + 23*x^4/A(x)^4 + 104*x^5/A(x)^5 + 537*x^6/A(x)^6 +...+ A080108(n)*x^n/A(x)^n +...

Prog

(PARI) {a(n)=local(A=1+x); for(i=1, n, A=sum(m=0, n, x^m/(A-m*x+x*O(x^n))^m)); polcoeff(A, n)}
for(n=0, 30, print1(a(n), ", "))

Crossrefs

Cf. A211207, A099947, A080108.

Sequence in context: A328507 A208733 A264899 * A320566 A205802 A117226

Adjacent sequences: A224783 A224784 A224785 * A224787 A224788 A224789

Keyword

nonn

Author

Paul D. Hanna, Apr 17 2013

Status

approved