A143553 G.f. satisfies: A(x) = 1 + x*A(x)^5*A(-x)^3.

1, 1, 2, 14, 50, 432, 1818, 17082, 77714, 763967, 3637718, 36786268, 180481258, 1860798032, 9324573430, 97502825964, 496344066386, 5245970686152, 27032002846992, 288124627083382, 1499144278319270, 16087838913122064

Offset

0,3

Links

Table of n, a(n) for n=0..21.

Formula

G.f. satisfies: A(x) + A(-x) = 1 + [A(x)*A(-x)] + x^2*[A(x)*A(-x)]^8.

Example

G.f. A(x) = 1 + x + 2*x^2 + 14*x^3 + 50*x^4 + 432*x^5 + 1818*x^6 +...
Related expansions:
A(x)^5 = 1 + 5*x + 20*x^2 + 120*x^3 + 635*x^4 + 4301*x^5 + 25360*x^6 +...
A(-x)^3 = 1 - 3*x + 9*x^2 - 55*x^3 + 252*x^4 - 1818*x^5 + 9560*x^6 -+...
A(x)*A(-x) = 1 + 3*x^2 + 76*x^4 + 2776*x^6 + 118940*x^8 +...
[A(x)*A(-x)]^8 = 1 + 24*x^2 + 860*x^4 + 36488*x^6 + 1700198*x^8 +...

Prog

(PARI) {a(n)=local(A=1+x*O(x^n)); for(i=0, n, A=1+x*A^5*subst(A^3, x, -x)); polcoeff(A, n)}

Crossrefs

Cf. A143550, A143551, A143552, A143554.

Sequence in context: A163796 A153978 A214908 * A341493 A064363 A363706

Adjacent sequences: A143550 A143551 A143552 * A143554 A143555 A143556

Keyword

nonn

Author

Paul D. Hanna, Aug 24 2008

Status

approved