A154836 G.f. satisfies: A(x) = x + A(x*A(x)/(1-x)) with A(0)=0.

1, 1, 2, 5, 13, 36, 104, 311, 955, 2994, 9542, 30818, 100633, 331657, 1101708, 3684785, 12398126, 41936805, 142520868, 486400191, 1666330558, 5728305895, 19754004806, 68317426480, 236893446915, 823435684539, 2868676129248

Offset

1,3

Links

Table of n, a(n) for n=1..27.

Example

G.f.: A(x) = x + x^2 + 2*x^3 + 5*x^4 + 13*x^5 + 36*x^6 + 104*x^7 +...
A(x*A(x)/(1-x)) = x^2 + 2*x^3 + 5*x^4 + 13*x^5 + 36*x^6 + 104*x^7 +...
Let G(x) = x*A(x)/(1-x) then
A(x) = x + G(x) + G(G(x)) + G(G(G(x))) + G(G(G(G(x)))) + ... where
G(x) = x^2 + 2*x^3 + 4*x^4 + 9*x^5 + 22*x^6 + 58*x^7 + 162*x^8 +...;
G(G(x)) = x^4 + 4*x^5 + 14*x^6 + 46*x^7 + 148*x^8 + 474*x^9 +...;
G(G(G(x))) = x^8 + 8*x^9 + 44*x^10 + 204*x^11 + 862*x^12 +...;
G(G(G(G(x)))) = x^16 + 16*x^17 + 152*x^18 + 1112*x^19 +...; ...

Prog

(PARI) {a(n)=local(A=x+x*O(x)); for(i=0, n, A=x+subst(A, x, x/(1-x)*A)); polcoeff(A, n)}

Crossrefs

Sequence in context: A246555 A366023 A136751 * A087626 A125094 A271941

Adjacent sequences: A154833 A154834 A154835 * A154837 A154838 A154839

Keyword

nonn

Author

Paul D. Hanna, Jan 16 2009

Status

approved