A119736 G.f. satisfies: A(x) = x + 2*x*A(A(x)) - x*A(x)*A(A(A(x))).

1, 2, 7, 36, 236, 1824, 15920, 152902, 1589049, 17664790, 208322454, 2590298272, 33798788538, 461078981884, 6556432452540, 96939246851454, 1487173494072195, 23630403273226874, 388278726368516603, 6588263758154705850

Offset

0,2

Links

Table of n, a(n) for n=0..19.

Formula

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

Example

Successive self-compositions of A(x) begin:
A(x) = x + 2*x^2 + 7*x^3 + 36*x^4 + 236*x^5 + 1824*x^6 + 15920*x^7 +...
A(A(x)) = x + 4*x^2 + 22*x^3 + 150*x^4 + 1191*x^5 + 10610*x^6 +...
A(A(A(x))) = x + 6*x^2 + 45*x^3 + 390*x^4 + 3753*x^5 + 39204*x^6 +...
A(A(A(A(x)))) = x + 8*x^2 + 76*x^3 + 804*x^4 + 9194*x^5 + 111828*x^6 +...
A(A(A(A(A(x))))) = x + 10*x^2 + 115*x^3 + 1440*x^4 + 19170*x^5 +...

Prog

(PARI) {a(n)=local(A=x+x*O(x^n)); for(i=1, n, A=x+2*x*subst(A, x, A)-x*A*subst(A, x, subst(A, x, A))); polcoeff(A, n)}

Crossrefs

Sequence in context: A018954 A019030 A212411 * A353166 A308750 A088715

Adjacent sequences: A119733 A119734 A119735 * A119737 A119738 A119739

Keyword

nonn

Author

Paul D. Hanna, Jun 15 2006

Status

approved