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Search: id:A143546
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| A143546 |
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G.f. satisfies: A(x) = 1 + x*A(x)^3*A(-x)^2. |
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+0
2
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| 1, 1, 1, 3, 5, 18, 35, 136, 285, 1155, 2530, 10530, 23751, 100688, 231880, 996336, 2330445, 10116873, 23950355, 104819165, 250543370, 1103722620, 2658968130, 11777187240, 28558343775, 127067830773, 309831575760, 1383914371728
(list; graph; listen)
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OFFSET
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0,4
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FORMULA
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G.f.: A(x) = G(x^2) + x*G(x^2)^3 where G(x) = 1 + x*G(x)^5 is the g.f. of A002294.
a(2n) = C(5n,n)/(4n+1); a(2n+1) = C(5n+2,n)*3/(4n+3).
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EXAMPLE
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G.f.: A(x) = 1 + x + x^2 + 3*x^3 + 5*x^4 + 18*x^5 + 35*x^6 + 136*x^7 +...
A(x) = 1 + x*A(x)^3*A(-x)^2 where
A(x)^3 = 1 + 3x + 6x^2 + 16x^3 + 39x^4 + 114x^5 + 304x^6 + 936x^7 +...
A(-x)^2 = 1 - 2x + 3x^2 - 8x^3 + 17x^4 - 52x^5 + 125x^6 - 408x^7 +...
Also, A(x) = G(x^2) + x*G(x^2)^3 where
G(x) = 1 + x + 5*x^2 + 35*x^3 + 285*x^4 + 2530*x^5 + 23751*x^6 +...
G(x)^3 = 1 + 3*x + 18*x^2 + 136*x^3 + 1155*x^4 + 10530*x^5 +...
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PROGRAM
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(PARI) {a(n)=local(A=1+O(x^(n+1))); for(i=0, n, A=1+x*A^3*subst(A^2, x, -x)); polcoeff(A, n)} (PARI) {a(n)=local(m=n\2, p=2*(n%2)+1); binomial(5*m+p-1, m)*p/(4*m+p)}
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CROSSREFS
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Cf. A002294, A118970.
Sequence in context: A007516 A039584 A136131 this_sequence A069066 A011964 A123793
Adjacent sequences: A143543 A143544 A143545 this_sequence A143547 A143548 A143549
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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 23 2008
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