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A143338 G.f. satisfies: A(x) = 1 + x*A(x)^3*A(-x). 3
1, 1, 2, 8, 26, 127, 478, 2536, 10250, 56900, 239880, 1370272, 5940054, 34607146, 153018932, 904441648, 4058644842, 24254529036, 110096276440, 663665021280, 3040205250984, 18455364854839, 85176971647470, 520059936017128 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..23.

EXAMPLE

G.f.: A(x) = 1 + x + 2*x^2 + 8*x^3 + 26*x^4 + 127*x^5 + 478*x^6 +...

Compare bisections of A(x)^2, A(x)^2*A(-x), and A(x)^4*A(-x)^2:

A(x)^2 = 1 + 2*x + 5*x^2 + 20*x^3 + 72*x^4 + 338*x^5 + 1378*x^6 + 6952*x^7 +...

A(x)^2*A(-x) = 1 + x + 5*x^2 + 11*x^3 + 72*x^4 + 191*x^5 + 1378*x^6 + 3979*x^7 +...

A(x)^4*A(-x)^2 = 1 + 2*x + 11*x^2 + 32*x^3 + 191*x^4 + 636*x^5 + 3979*x^6 +...

Related expansions:

A(x)^3 = 1 + 3*x + 9*x^2 + 37*x^3 + 144*x^4 + 669*x^5 + 2882*x^6 + 14229*x^7 +...

A(x)^3*A(-x) = 1 + 2*x + 8*x^2 + 26*x^3 + 127*x^4 + 478*x^5 + 2536*x^6 +...

A(x)^3*A(-x)^2 = 1 + x + 8*x^2 + 14*x^3 + 127*x^4 + 264*x^5 + 2536*x^6 +...

PROG

(PARI) {a(n)=local(A=1+x+O(x^21)); for(i=0, n, A=1+x*A^3*subst(A, x, -x)); polcoeff(A, n)}

CROSSREFS

Sequence in context: A150708 A150709 A130613 * A027267 A060414 A087241

Adjacent sequences:  A143335 A143336 A143337 * A143339 A143340 A143341

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Aug 09 2008

STATUS

approved

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Last modified May 25 04:50 EDT 2019. Contains 323539 sequences. (Running on oeis4.)