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A188664
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a(n) = 2A(n)/C(n) where A(n) = A180874(n) and C(n) = Catalan(n) = A000108(n).
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2
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2, 1, 2, 8, 52, 495, 6470, 111034, 2419928, 65269092, 2133844440, 83133090480, 3805035352536, 202147745618247, 12336516593999598, 857054350280418290, 67247553674224203280, 5917723267088513913032, 580407202154922558537264, 63093021853191022229671056, 7563270705677373923076693840
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OFFSET
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1,1
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COMMENTS
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For properties of these numbers including a recurrence, see the Lassalle reference.
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LINKS
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MAPLE
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A000108 := proc(n) binomial(2*n, n)/(1+n) ; end proc:
A180874 := proc(n) option remember; if n = 1 then 1 else A000108(n)+add((-1)^j*binomial(2*n-1, 2*j-1)*procname(j)*A000108(n-j), j=1..n-1) ; %*(-1)^(n-1) ; end if; end proc:
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MATHEMATICA
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c = CatalanNumber;
A[n_] := A[n] = (-1)^(n - 1)*(c[n] + Sum[(-1)^j*Binomial[2*n - 1, 2*j - 1]*A[j]*c[n - j], {j, 1, n - 1}]);
a[n_] := 2 A[n]/c[n];
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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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