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A205320 G.f.: A(x) = x + x*ITERATE^2(x + x*ITERATE^4(x + x*ITERATE^6(x + x*ITERATE^8(x + ...)))), where ITERATE^n(F(x)) denotes the n-th iteration of F(x), and the nesting of even iterations continue indefinitely. 2
1, 1, 2, 10, 93, 1328, 26122, 662688, 20768108, 780250074, 34376313158, 1746482796840, 100964618760718, 6570171769295176, 476961360708388461, 38334059714026619028, 3388777691630610169520, 327633680973521183134333, 34470692910252290655821322, 3929174185110859040857539276 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

Table of n, a(n) for n=1..20.

EXAMPLE

G.f.: A(x) = x + x^2 + 2*x^3 + 10*x^4 + 93*x^5 + 1328*x^6 + 26122*x^7 +...

where A(x) is generated by nesting even 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(x)))))));

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

The coefficients in the respective series begin:

B: [1, 1, 4, 36, 522, 10528, 273524, 8744724, 333829460, ...];

C: [1, 1, 6, 78, 1551, 41104, 1355350, 53445516, 2457584702, ...];

D: [1, 1, 8, 136, 3444, 113600, 4570568, 216110200, 11732501680, ...];

E: [1, 1, 10, 210, 6465, 255600, 12172130, 673488008, 42339965808, ...];

F: [1, 1, 12, 300, 10878, 501728, 27635132, 1754547372, 125631525316, ...];

G: [1, 1, 14, 406, 16947, 893648, 55924974, 4010847764, 322635273394, ...];

H: [1, 1, 16, 528, 24936, 1480064, 103765520, 8300468272, 741606109248, ...]; ...

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}

/* G.f. A(x) results from nested iterations of shifted series: */

{a(n)=local(A=x); for(k=0, n, A=x + x*ITERATE(2*n-2*k+2, A, n)); polcoeff(A, n)}

CROSSREFS

Cf. A195192, A205319.

Sequence in context: A293709 A063393 A260339 * A254243 A026025 A231375

Adjacent sequences:  A205317 A205318 A205319 * A205321 A205322 A205323

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Jan 25 2012

STATUS

approved

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Last modified December 14 17:32 EST 2019. Contains 329979 sequences. (Running on oeis4.)