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A122894 Coefficient of x^(2^(n-1)) in the n-th self-composition of (x+x^2) for n>=1. 1
1, 2, 9, 258, 293685, 531124770570, 2439717292075827330588969, 72554628124279239546273779187960042205300343234178 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Originated by Ralf Stephan in A092123 as the 2^(n-1)th coefficient in the expansion of P(0)=x, P(n+1)=P(n)*[1+P(n)] (equivalent definition). Next term is too large to include.

LINKS

Table of n, a(n) for n=1..8.

EXAMPLE

a(1) = 1 = [x^1] (x + x^2).

a(2) = 2 = [x^2] (x + 2*x^2 + 2*x^3 + x^4).

a(3) = 9 = [x^4] (x + 3*x^2 + 6*x^3 + 9*x^4 + 10*x^5 + 8*x^6 + 4*x^7 + x^8).

PROG

(PARI) {a(n)=local(F=x+x^2, G=x+x*O(x^(2^(n-1)))); if(n<1, 0, for(i=1, n, G=subst(F, x, G)); return(polcoeff(G, 2^(n-1), x)))}

CROSSREFS

Cf. A092123, A122893; A122888.

Sequence in context: A267408 A165797 A011823 * A042675 A015177 A005271

Adjacent sequences:  A122891 A122892 A122893 * A122895 A122896 A122897

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Sep 19 2006

STATUS

approved

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Last modified March 18 19:58 EDT 2019. Contains 321293 sequences. (Running on oeis4.)