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A212491 G.f.: A(x) = x + x*ITERATE^2(x + x*ITERATE^4(x + x*ITERATE^8(x + x*ITERATE^16(x + ...)))), where ITERATE^n(F(x)) denotes the n-th iteration of F(x), and the nesting of iterations continue indefinitely. 0
1, 1, 2, 10, 109, 2344, 95526, 7321508, 1062894966, 295821381776, 159750645147982, 169055785061863986, 353149667541498542122, 1463495730873823283553016, 12070551778811708797824867546, 198534598750957942596957876692320, 6519958358404237723197281898833187776 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

Table of n, a(n) for n=1..17.

EXAMPLE

G.f.: A(x) = x + x^2 + 2*x^3 + 10*x^4 + 109*x^5 + 2344*x^6 + 95526*x^7 +...

where A(x) is generated by nesting 2^n-th iterations of shifted series:

A(x) = x + x*B(B(x));

B(x) = x + x*C(C(C(C(x))));

C(x) = x + x*D(D(D(D(D(D(D(D(x))))))));

D(x) = x + x*E(E(E(E(E(E(E(E(E(E(E(E(E(E(E(E(x)))))))))))); ...

The above series begin:

B(x) = x + x^2 + 4*x^3 + 44*x^4 + 1006*x^5 + 43392*x^6 + 3459214*x^7 +...

C(x) = x + x^2 + 8*x^3 + 184*x^4 + 8620*x^5 + 746176*x^6 + 117816292*x^7 +...

D(x) = x + x^2 + 16*x^3 + 752*x^4 + 71320*x^5 + 12374144*x^6 +...

E(x) = x + x^2 + 32*x^3 + 3040*x^4 + 580144*x^5 + 201551104*x^6 +...

PROG

PARI) /* Define the (2^n)-th iteration of function F: */

{ITERATE2(n, F, p=#F)=local(G=F); for(i=1, n, G=subst(G, 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=ITERATE2(n-k, x + x*A, n)); polcoeff(A, n)}

for(n=1, 20, print1(a(n), ", "))

CROSSREFS

Cf. A195192, A205320, A205319.

Sequence in context: A003167 A240625 A062412 * A006608 A066205 A113147

Adjacent sequences:  A212488 A212489 A212490 * A212492 A212493 A212494

KEYWORD

nonn

AUTHOR

Paul D. Hanna, May 18 2012

STATUS

approved

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Last modified November 19 18:39 EST 2019. Contains 329323 sequences. (Running on oeis4.)