A143552 G.f. satisfies: A(x) = 1 + x*A(x)^5*A(-x)^2.

1, 1, 3, 22, 115, 1048, 6418, 63784, 421195, 4386273, 30271136, 324599018, 2306033386, 25228297188, 182938978344, 2030788315648, 14952369357211, 167836915812087, 1250429798513035, 14158770843121424, 106483223789898776

Offset

0,3

Links

Table of n, a(n) for n=0..20.

Formula

G.f. satisfies: A(x) + A(-x) = 1 + [A(x)*A(-x)] + x^2*[A(x)*A(-x)]^7.

Example

G.f. A(x) = 1 + x + 3*x^2 + 22*x^3 + 115*x^4 + 1048*x^5 + 6418*x^6 +...
Related expansions:
A(x)^5 = 1 + 5*x + 25*x^2 + 180*x^3 + 1200*x^4 + 9851*x^5 + 73195*x^6 +...
A(-x)^2 = 1 - 2*x + 7*x^2 - 50*x^3 + 283*x^4 - 2458*x^5 + 16106*x^6 -+...
A(x)*A(-x) = 1 + 5*x^2 + 195*x^4 + 10946*x^6 + 720443*x^8 +...
[A(x)*A(-x)]^7 = 1 + 35*x^2 + 1890*x^4 + 121947*x^6 + 8674036*x^8 +...

Prog

(PARI) {a(n)=local(A=1+x*O(x^n)); for(i=0, n, A=1+x*A^5*subst(A^2, x, -x)); polcoeff(A, n)}

Crossrefs

Cf. A143550, A143551, A143553, A143554.

Sequence in context: A309000 A352027 A061182 * A006283 A232017 A100511

Adjacent sequences: A143549 A143550 A143551 * A143553 A143554 A143555

Keyword

nonn

Author

Paul D. Hanna, Aug 24 2008

Status

approved