A140046 G.f. satisfies: A(x) = x/(1 - A(x+x^2)).

1, 1, 3, 10, 41, 186, 922, 4911, 27830, 166656, 1049410, 6922476, 47698148, 342483885, 2557538781, 19829608532, 159393394129, 1326509171669, 11415703608635, 101473987987073, 930688926616454, 8798656042121634

Offset

1,3

Links

Table of n, a(n) for n=1..22.

Example

G.f.: A(x) = x + x^2 + 3*x^3 + 10*x^4 + 41*x^5 + 186*x^6 + 922*x^7 +...
A(x+x^2) = x + 2*x^2 + 5*x^3 + 20*x^4 + 90*x^5 + 454*x^6 + 2488*x^7 +...
Let B(x) = x + x^2; define B_{n+1}(x) = B( B_{n}(x) ) with B_0(x)=x;
then g.f. A(x) equals the continued fraction:
A(x) = x/(1 - B(x)/(1 - B_2(x)/(1 - B_3(x)/(1 - B_4(x)/(1 - ...)))))
where B_{n}(x) begin:
B_2(x) = x + 2*x^2 + 2*x^3 + x^4 ;
B_3(x) = x + 3*x^2 + 6*x^3 + 9*x^4 + 10*x^5 + 8*x^6 + 4*x^7 + x^8 ;
B_4(x) = x + 4*x^2 + 12*x^3 + 30*x^4 + 64*x^5 + 118*x^6 + 188*x^7 +...;
B_5(x) = x + 5*x^2 + 20*x^3 + 70*x^4 + 220*x^5 + 630*x^6 + 1656*x^7 +...

Prog

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

Crossrefs

Cf. A127782.

Sequence in context: A260789 A151082 A151083 * A260772 A325059 A116540

Adjacent sequences: A140043 A140044 A140045 * A140047 A140048 A140049

Keyword

nonn

Author

Paul D. Hanna, May 09 2008

Status

approved