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A163135 G.f. A(x) equals an infinite symmetric composition of functions x/(1-x^n), n=1,2,3,... 2
1, 2, 6, 20, 69, 245, 885, 3235, 11923, 44211, 164694, 615721, 2308499, 8675121, 32661637, 123161206, 465018949, 1757672820, 6649722003, 25177228890, 95390000028, 361616383623, 1371545371027, 5204283449684, 19754979558587 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Limit a(n+1)/a(n) ~ 3.80825961708875...

LINKS

Table of n, a(n) for n=1..25.

FORMULA

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

EXAMPLE

G.f.: A(x) = x + 2*x^2 + 6*x^3 + 20*x^4 + 69*x^5 + 245*x^6 +...

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

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

(2) x/(1-x) o x/(1-x^2) o x/(1-x^2) o x/(1-x) = (x-3*x^2+2*x^3)/(1-5*x+6*x^2-x^4);

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

PROG

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

CROSSREFS

Cf. A163134.

Sequence in context: A217782 A026029 A078483 * A331951 A047036 A199248

Adjacent sequences:  A163132 A163133 A163134 * A163136 A163137 A163138

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Aug 12 2009

STATUS

approved

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Last modified November 27 20:49 EST 2021. Contains 349395 sequences. (Running on oeis4.)