AUTHOR
_Paul D. Hanna (pauldhanna(AT)juno.com), _, Aug 24 2008
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Revision History for A143563
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NAME
G.f. satisfies: A(x) = 1 + x*A(x)^4/A(-x)^2.
DATA
1, 1, 6, 29, 242, 1554, 14476, 104061, 1024122, 7818662, 79523444, 630256402, 6552401972, 53271202948, 562560238232, 4658979320605, 49780348483530, 418091057783582, 4508111500966628, 38281314209625862, 415790041176520092
OFFSET
0,3
FORMULA
G.f. satisfies: A(x) + A(-x) = 1 + A(x)*A(-x) + x^2*A(x)^2*A(-x)^2.
EXAMPLE
G.f. A(x) = 1 + x + 6*x^2 + 29*x^3 + 242*x^4 + 1554*x^5 + 14476*x^6 +...
A(x)*A(-x) = 1 + 11*x^2 + 462*x^4 + 27907*x^6 + 1982266*x^8 +...
A(x)^2*A(-x)^2 = 1 + 22*x^2 + 1045*x^4 + 65978*x^6 + 4791930*x^8 +...
PROG
(PARI) {a(n)=local(A=1+x*O(x^n)); for(i=0, n, A=1+x*A^4/subst(A^2, x, -x)); polcoeff(A, n)}
KEYWORD
nonn
AUTHOR
Paul D. Hanna (pauldhanna(AT)juno.com), Aug 24 2008
STATUS
approved