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Search: id:A143559
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| A143559 |
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G.f. satisfies: A(x) = 1 + x*A(x)^6/A(-x)^6. |
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+0
5
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| 1, 1, 12, 72, 1012, 9552, 148764, 1609496, 26398020, 305821344, 5174354988, 62479377384, 1079265357204, 13399747245040, 234917433809724, 2975608178304696, 52748683164797668, 678307369324850496
(list; graph; listen)
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OFFSET
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0,3
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FORMULA
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G.f. satisfies: A(x) = 1 + x^2/(1 - A(-x)).
G.f. satisfies: (A(x) - 1)^5 = ( 1 - (1+x^2)/A(x) )^6/x = x^5*A(x)^30/A(-x)^30.
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EXAMPLE
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G.f. A(x) = 1 + x + 12*x^2 + 72*x^3 + 1012*x^4 + 9552*x^5 + 148764*x^6 +...
A(x)/A(-x) = 1 + 2*x + 2*x^2 + 122*x^3 + 242*x^4 + 16002*x^5 + 38962*x^6 +...
A(x)^5/A(-x)^5 = 1 + 10*x + 50*x^2 + 770*x^3 + 6450*x^4 + 109802*x^5 +...
where 1 - (1+x^2)/A(x) = x*A(x)^5/A(-x)^5.
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PROGRAM
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(PARI) {a(n)=local(A=1+x*O(x^n)); for(i=0, n, A=1+x*A^6/subst(A^6, x, -x)); polcoeff(A, n)}
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CROSSREFS
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Cf. A143555, A143556, A143557, A143558.
Sequence in context: A088166 A138402 A108734 this_sequence A120793 A120783 A103475
Adjacent sequences: A143556 A143557 A143558 this_sequence A143560 A143561 A143562
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KEYWORD
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nonn
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AUTHOR
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Paul D. Hanna (pauldhanna(AT)juno.com), Aug 24 2008
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