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A192400
G.f. A(x) satisfies A(x) = 1 + Sum_{n>=1} A(x)^n * x^(2*n-1)/(1 - x^(2*n-1)).
3
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
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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
