A195192 G.f.: A(x) = x + x*ITERATE^2(x + x*ITERATE^3(x + x*ITERATE^4(x + x*ITERATE^5(x + ...)))), where ITERATE^n(F(x)) denotes the n-th iteration of F(x), and the nested iterations continue indefinitely.

1, 1, 2, 8, 52, 480, 5811, 87768, 1599189, 34317476, 851848787, 24117965057, 770085965621, 27472955220394, 1086491917437511, 47313129973804599, 2255470786017010440, 117103678748934306726, 6591945250191262271448, 400690880212910627734513, 26204671530683391316131317

Offset

1,3

Links

Paul D. Hanna, Table of n, a(n) for n = 1..100

Example

G.f.: A(x) = x + x^2 + 2*x^3 + 8*x^4 + 52*x^5 + 480*x^6 + 5811*x^7 +...
where A(x) is generated by nested iterations of shifted series:
A(x) = x + x*B(B(x)), where
B(x) = x + x^2 + 3*x^3 + 18*x^4 + 165*x^5 + 2034*x^6 + 31500*x^7 +...;
B(x) = x + x*C(C(C(x))), where
C(x) = x + x^2 + 4*x^3 + 32*x^4 + 380*x^5 + 5904*x^6 + 112528*x^7 +...;
C(x) = x + x*D(D(D(D(x)))), where
D(x) = x + x^2 + 5*x^3 + 50*x^4 + 730*x^5 + 13720*x^6 + 311730*x^7 +...;
D(x) = x + x*E(E(E(E(E(x))))), where
E(x) = x + x^2 + 6*x^3 + 72*x^4 + 1248*x^5 + 27552*x^6 + 728175*x^7 +...;
E(x) = x + x*F(F(F(F(F(F(x)))))), where
F(x) = x + x^2 + 7*x^3 + 98*x^4 + 1967*x^5 + 49910*x^6 + 1505546*x^7 +...;
F(x) = x + x*G(G(G(G(G(G(G(x))))))), where
G(x) = x + x^2 + 8*x^3 + 128*x^4 + 2920*x^5 + 83744*x^6 + 2840520*x^7 +...;
G(x) = x + x*H(H(H(H(H(H(H(H(x)))))))), where
H(x) = x + x^2 + 9*x^3 + 162*x^4 + 4140*x^5 + 132444*x^6 + 4991148*x^7 +...; ...

Prog

(PARI) /* Define the n-th iteration of function F: */
{ITERATE(n, F, p)=local(G=x); for(i=1, n, G=subst(F, x, G+x*O(x^p))); G}
/* A(x) results from nested iterations of shifted series: */
{a(n)=local(A=x); for(k=0, n, A=ITERATE(n-k+1, x + x*A, n)); polcoeff(A, n)}

Crossrefs

Sequence in context: A300697 A277499 A089467 * A103239 A209307 A323843

Adjacent sequences: A195189 A195190 A195191 * A195193 A195194 A195195

Keyword

nonn

Author

Paul D. Hanna, Sep 11 2011

Status

approved