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A163134
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G.f. A(x) equals an infinite symmetric composition of functions x/(1-x^n), n=1,2,3,...
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2
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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; internal format)
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OFFSET
| 1,2
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COMMENTS
| Limit a(n+1)/a(n) seems to exist, approximately = 4.75...
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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...
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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); ...
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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)))}
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CROSSREFS
| Cf. A163135.
Sequence in context: A128729 A006027 A049124 * A150128 A148480 A194950
Adjacent sequences: A163131 A163132 A163133 * A163135 A163136 A163137
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KEYWORD
| nonn
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AUTHOR
| Paul D. Hanna (pauldhanna(AT)juno.com), Aug 12 2009
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