A154835 G.f. satisfies: A(x) = x + A((x+x^2)*A(x)) with A(0)=0.

1, 1, 2, 4, 10, 26, 72, 205, 597, 1770, 5329, 16253, 50112, 155939, 489111, 1544723, 4908164, 15678715, 50323541, 162213311, 524895810, 1704407999, 5552027379, 18137964251, 59412854411, 195090277189, 642056206297, 2117485840188

Offset

1,3

Links

Table of n, a(n) for n=1..28.

Example

G.f.: A(x) = x + x^2 + 2*x^3 + 4*x^4 + 10*x^5 + 26*x^6 + 72*x^7 +...
A((x+x^2)*A(x)) = x^2 + 2*x^3 + 4*x^4 + 10*x^5 + 26*x^6 + 72*x^7 +...
Let G(x) = (x+x^2)*A(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 + 3*x^4 + 6*x^5 + 14*x^6 + 36*x^7 + 98*x^8 +...;
G(G(x)) = x^4 + 4*x^5 + 12*x^6 + 36*x^7 + 106*x^8 + 312*x^9 +...;
G(G(G(x))) = x^8 + 8*x^9 + 40*x^10 + 168*x^11 + 646*x^12 +...;
G(G(G(G(x)))) = x^16 + 16*x^17 + 144*x^18 + 976*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: A125108 A075864 A180023 * A049145 A102407 A358455

Adjacent sequences: A154832 A154833 A154834 * A154836 A154837 A154838

Keyword

nonn

Author

Paul D. Hanna, Jan 16 2009

Status

approved