A192400 G.f. A(x) satisfies A(x) = 1 + Sum_{n>=1} A(x)^n * x^(2*n-1)/(1 - x^(2*n-1)).

1, 1, 2, 5, 11, 26, 64, 158, 399, 1027, 2675, 7052, 18788, 50487, 136711, 372687, 1021942, 2816873, 7800510, 21691134, 60543553, 169561453, 476351239, 1342002198, 3790565335, 10732246631, 30453309502, 86589559266, 246672752090

Offset

0,3

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=1.

Links

Table of n, a(n) for n=0..28.

Formula

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

Example

G.f.: A(x) = 1 + x + 2*x^2 + 5*x^3 + 11*x^4 + 26*x^5 + 64*x^6 +...
which satisfies the following relations:
A(x) = 1 + A(x)*x/(1-x) + A(x)^2*x^3/(1-x^3) + A(x)^3*x^5/(1-x^5) +...
A(x) = 1 + A(x)*x/(1-A(x)*x^2) + A(x)*x^2/(1-A(x)*x^4) + 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*x^(2*m-1)/(1-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, A*x^m/(1-A*x^(2*m)+x*O(x^n)))); polcoeff(A, n)}

Crossrefs

Cf. A192401, A192402.

Sequence in context: A082397 A051286 A192475 * A308154 A182053 A306563

Adjacent sequences: A192397 A192398 A192399 * A192401 A192402 A192403

Keyword

nonn

Author

Paul D. Hanna, Jun 30 2011

Status

approved