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A349011
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G.f. A(x) satisfies: A(x) = (1 - x * A(-x)) / (1 - 2 * x * A(x)).
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1
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1, 1, 5, 17, 105, 433, 2925, 13185, 93425, 443009, 3233205, 15840209, 117950745, 591187953, 4466545245, 22766535297, 173906505825, 897941153665, 6918379345125, 36089242700049, 279988660639305, 1472715584804529, 11490841104036045, 60857608450349313, 477104721264920145
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OFFSET
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0,3
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LINKS
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FORMULA
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a(0) = 1; a(n) = (-1)^n * a(n-1) + 2 * Sum_{k=0..n-1} a(k) * a(n-k-1).
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MAPLE
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option remember ;
if n = 0 then
1;
else
(-1)^n*procname(n-1)+2*add(procname(k)*procname(n-k-1), k=0..n-1) ;
end if;
end proc:
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MATHEMATICA
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nmax = 24; A[_] = 0; Do[A[x_] = (1 - x A[-x])/(1 - 2 x A[x]) + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]
a[0] = 1; a[n_] := a[n] = (-1)^n a[n - 1] + 2 Sum[a[k] a[n - k - 1], {k, 0, n - 1}]; Table[a[n], {n, 0, 24}]
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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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