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A163134 G.f. A(x) equals an infinite symmetric composition of functions x/(1-x^n), n=1,2,3,... 2
1, 2, 6, 20, 71, 266, 1033, 4133, 16919, 70543, 298461, 1277895, 5525308, 24086364, 105730896, 466907516, 2072662801, 9243364577, 41392064353, 186040133239, 838962247305, 3794801298127, 17211872676042, 78262816746849 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Limit a(n+1)/a(n) seems to exist, approximately = 4.75...

LINKS

Table of n, a(n) for n=1..24.

FORMULA

A(x) = ...o x/(1-x^3) o x/(1-x^2) o x/(1-x) o (x) o x/(1-x) o x/(1-x^2) o x/(1-x^3) o...

EXAMPLE

G.f.: A(x) = x + 2*x^2 + 6*x^3 + 20*x^4 + 71*x^5 + 266*x^6 +...

A(x) is the limit of compositions beginning in the following manner:

(1) x/(1-x) o x/(1-x) = x/(1-2*x);

(2) x/(1-x^2) o x/(1-x) o x/(1-x) o x/(1-x^2) = (x-2*x^2-x^3)/(1-4*x+x^2+4*x^3+x^4);

(3) x/(1-x^3) o x/(1-x^2) o x/(1-x) o x/(1-x) o x/(1-x^2) o x/(1-x^3); ...

PROG

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

CROSSREFS

Cf. A163135.

Sequence in context: A049124 A275756 A301627 * A150128 A148480 A194950

Adjacent sequences:  A163131 A163132 A163133 * A163135 A163136 A163137

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Aug 12 2009

STATUS

approved

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Last modified May 20 21:39 EDT 2022. Contains 353876 sequences. (Running on oeis4.)