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A143927
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G.f. satisfies: A(x) = (1 + x*A(x) + x^2*A(x)^2)^2.
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13
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1, 2, 7, 28, 123, 572, 2769, 13806, 70414, 365636, 1926505, 10273870, 55349155, 300783420, 1646828655, 9075674700, 50304255210, 280248358964, 1568399676946, 8813424968192, 49709017472751, 281306750922072, 1596802663432503
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OFFSET
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0,2
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LINKS
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FORMULA
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a(n) = (1/(n+1))*Sum_{j=0..2*n+2} (binomial(j,2*j-3*n-4)*binomial(2*n+2 ,j)). - Vladimir Kruchinin, Dec 24 2010
The g.f. A(x) satisfies 1 + x*A'(x)/A(x) = 1 + 2*x + 10*x^2 + 50*x^3 + 266*x^3 + ..., the g.f. of A027908. - Peter Bala, Aug 03 2023
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MATHEMATICA
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Table[GegenbauerC[n, -2n-2, -1/2]/(n+1), {n, 0, 12}] (* Emanuele Munarini, Oct 20 2016 *)
n = 20;
A = Sum[a[k] x^k, {k, 0, n}] + x O[x]^n;
Table[a[k], {k, 0, n}] /. Reverse[Solve[LogicalExpand[(1 + x A + x^2 A^2)^2 == A]]] (* Emanuele Munarini, Oct 20 2016 *)
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PROG
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(PARI) {a(n)=local(A=1+x+x*O(x^n)); for(i=0, n, A=(1+x*A+x^2*A^2)^2); polcoeff(A, n)}
(Maxima) makelist(ultraspherical(n, -2*n-2, -1/2)/(n+1), n, 0, 12); /* Emanuele Munarini, Oct 20 2016 */
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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