A192402 G.f. A(x) satisfies A(x) = 1 + Sum_{n>=1} A(x)^n * 2*x^(2*n-1)/(1 - 2*x^(2*n-1)).

1, 2, 8, 34, 140, 586, 2476, 10522, 45048, 194210, 842672, 3678946, 16155140, 71328210, 316536532, 1411398138, 6321140080, 28426660498, 128325523272, 581349815466, 2642337533500, 12046547596514, 55076433751372, 252470682559914

Offset

0,2

Comments

Related q-series identity:

Sum_{n>=1} y^n*z*q^(2*n-1)/(1-z*q^(2*n-1)) = Sum_{n>=1} z^n*y*q^n/(1-y*q^(2*n)); here q=x, y=A(x), z=2.

Links

Table of n, a(n) for n=0..23.

Formula

G.f. satisfies: A(x) = 1 + Sum_{n>=1} 2^n*A(x)*x^n/(1 - A(x)*x^(2*n)).

Example

G.f.: A(x) = 1 + 2*x + 8*x^2 + 34*x^3 + 140*x^4 + 586*x^5 + 2476*x^6 +...
which satisfies the following relations:
A(x) = 1 + A(x)*2*x/(1-2*x) + A(x)^2*2*x^3/(1-2*x^3) + A(x)^3*2*x^5/(1-2*x^5) +...
A(x) = 1 + 2*A(x)*x/(1-A(x)*x^2) + 4*A(x)*x^2/(1-A(x)*x^4) + 8*A(x)*x^3/(1-A(x)*x^6) +...

Prog

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

Crossrefs

Cf. A192400, A192403.

Sequence in context: A345757 A369836 A228655 * A014445 A113440 A296227

Adjacent sequences: A192399 A192400 A192401 * A192403 A192404 A192405

Keyword

nonn

Author

Paul D. Hanna, Jun 30 2011

Status

approved