A163134 G.f. A(x) equals an infinite symmetric composition of functions x/(1-x^n), n=1,2,3,...

1, 2, 6, 20, 71, 266, 1033, 4133, 16919, 70543, 298461, 1277895, 5525308, 24086364, 105730896, 466907516, 2072662801, 9243364577, 41392064353, 186040133239, 838962247305, 3794801298127, 17211872676042, 78262816746849

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 * A370446 A150128 A148480

Adjacent sequences: A163131 A163132 A163133 * A163135 A163136 A163137

Keyword

nonn

Author

Paul D. Hanna, Aug 12 2009

Status

approved