A154259 G.f. A(x) satisfies: A(x) = x + 2*x*A(x) + 3*x^2*A(A(x)) + 4*x^3*A(A(A(x))) +...

1, 2, 7, 30, 155, 950, 6706, 52996, 459256, 4303020, 43163392, 460170882, 5184956805, 61468942912, 763967696243, 9924157671028, 134400823231643, 1893397004671954, 27693154054839058, 419804185629085664

Offset

1,2

Links

Table of n, a(n) for n=1..20.

Example

G.f.: A(x) = x + 2*x*A(x) + 3*x^2*A(A(x)) + 4*x^3*A(A(A(x))) +...
where the initial iterations of the g.f. A(x) begin:
A(x) = x + 2*x^2 + 7*x^3 + 30*x^4 + 155*x^5 + 950*x^6 + 6706*x^7 +...;
A(A(x)) = x + 4*x^2 + 22*x^3 + 138*x^4 + 957*x^5 + 7242*x^6 +...;
A(A(A(x))) = x + 6*x^2 + 45*x^3 + 372*x^4 + 3294*x^5 + 30858*x^6 +...;
A(A(A(A(x)))) = x + 8*x^2 + 76*x^3 + 780*x^4 + 8438*x^5 + 95156*x^6 +...;
A(A(A(A(A(x))))) = x + 10*x^2 + 115*x^3 + 1410*x^4 + 18045*x^5 +...; ...
so: a(1)=1, a(2)=2, a(3) = 2*2 + 3 = 7, a(4) = 2*7 + 3*4 + 4 = 30, ...

Prog

(PARI) {a(n)=local(F=x+x*O(x^n), G=F, H=x); for(i=1, n, for(k=1, n, G=subst(F, x, G); H=H+(k+1)*x^k*G); F=H; G=x+x*O(x^n); H=G); polcoeff(F, n)}

Crossrefs

Cf. A120567.

Sequence in context: A321735 A030975 A144495 * A066114 A088128 A001053

Adjacent sequences: A154256 A154257 A154258 * A154260 A154261 A154262

Keyword

nonn

Author

Paul D. Hanna, Jan 05 2009

Status

approved