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A213009 G.f. A(x) satisfies: A(A(x)) = x+x^2 + x*A(A(A(A(x)))). 5
1, 1, 1, 5, 21, 125, 825, 6133, 49925, 439417, 4142945, 41544161, 440710117, 4924691541, 57766255689, 709205703565, 9090541134373, 121389729560633, 1685431945085489, 24289856880005441, 362776874949660485, 5606980244843123077, 89560387072919814553 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

Given g.f. A(x), A(A(x)) equals the g.f. of A213010.

LINKS

Paul D. Hanna, Table of n, a(n) for n = 1..256

FORMULA

a(n) == 1 (mod 4).

EXAMPLE

G.f.: A(x) = x + x^2 + x^3 + 5*x^4 + 21*x^5 + 125*x^6 + 825*x^7 +...

where

A(A(x)) = x + 2*x^2 + 4*x^3 + 16*x^4 + 80*x^5 + 480*x^6 + 3296*x^7 +...

A(A(A(A(x)))) = x + 4*x^2 + 16*x^3 + 80*x^4 + 480*x^5 + 3296*x^6 +...

PROG

(PARI) {a(n)=local(A=x+x^2, B=x+2*x^2); for(i=1, n, B=x+x^2+x*subst(B, x, B+x*O(x^n)));

for(i=1, n, A=(A+subst(B, x, serreverse(A+x*O(x^n))))/2); polcoeff(A, n)}

for(n=1, 31, print1(a(n), ", "))

CROSSREFS

Cf. A213010, A215115, A215117, A215119.

Sequence in context: A124311 A353736 A208593 * A316102 A352388 A050910

Adjacent sequences: A213006 A213007 A213008 * A213010 A213011 A213012

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Jun 01 2012

STATUS

approved

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Last modified December 4 20:24 EST 2022. Contains 358568 sequences. (Running on oeis4.)