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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. 4
1, 1, 2, 8, 52, 480, 5811, 87768, 1599189, 34317476, 851848787, 24117965057, 770085965621, 27472955220394, 1086491917437511, 47313129973804599, 2255470786017010440, 117103678748934306726, 6591945250191262271448, 400690880212910627734513, 26204671530683391316131317 (list; graph; refs; listen; history; text; internal format)
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

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Last modified July 27 15:49 EDT 2021. Contains 346308 sequences. (Running on oeis4.)