The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A192401 G.f. A(x) satisfies A(x) = 1 + Sum_{n>=1} A(x)^n * x^n/(1 - x^(2*n)). 6
 1, 1, 2, 6, 16, 49, 156, 512, 1728, 5959, 20886, 74204, 266624, 967141, 3536814, 13025478, 48266972, 179831935, 673258626, 2531481990, 9555606112, 36196916933, 137554950152, 524265889839, 2003513188296, 7675473295796, 29471911733772 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Related q-series identity: Sum_{n>=1} z^n*y*q^n/(1-y*q^(2*n)) = Sum_{n>=1} y^n*z*q^(2*n-1)/(1-z*q^(2*n-1)); here q=x, y=1, z=A(x). LINKS FORMULA G.f. satisfies: A(x) = 1 + Sum_{n>=1} A(x)*x^(2*n-1)/(1 - A(x)*x^(2*n-1)). EXAMPLE G.f.: A(x) = 1 + x + 2*x^2 + 6*x^3 + 16*x^4 + 49*x^5 + 156*x^6 +... which satisfies the following relations: A(x) = 1 + A(x)*x/(1-x^2) + A(x)^2*x^2/(1-x^4) + A(x)^3*x^3/(1-x^6) +... A(x) = 1 + A(x)*x/(1-A(x)*x) + A(x)*x^3/(1-A(x)*x^3) + A(x)*x^5/(1-A(x)*x^5) +... PROG (PARI) {a(n)=local(A=1+x); for(i=1, n, A=1+sum(m=1, n, A^m*x^m/(1-x^(2*m)+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^(2*m-1)/(1-A*x^(2*m-1)+x*O(x^n)))); polcoeff(A, n)} CROSSREFS Cf. A192400, A192403. Sequence in context: A079565 A052890 A052814 * A151445 A213429 A195645 Adjacent sequences:  A192398 A192399 A192400 * A192402 A192403 A192404 KEYWORD nonn AUTHOR Paul D. Hanna, Jun 30 2011 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified May 7 00:22 EDT 2021. Contains 343609 sequences. (Running on oeis4.)