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A029759
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Number of permutations which are the union of an increasing and a decreasing subsequence.
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6
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1, 1, 2, 6, 22, 86, 340, 1340, 5254, 20518, 79932, 311028, 1209916, 4707964, 18330728, 71429176, 278586182, 1087537414, 4249391468, 16618640836, 65048019092, 254814326164, 998953992728, 3919041821896, 15385395144092, 60438585676636
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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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D-finite with recurrence: n*a(n) +(-9*n+8)*a(n-1) +2*(13*n-23)*a(n-2) +12*(-2*n+5)*a(n-3)=0. - R. J. Mathar, Aug 24 2013
a(n) = (binomial(2*n, n)*(hypergeom([1, n+1/2], [n+1], 2) + 2) + i*2^n)/2, where i is the imaginary unit. - Peter Luschny, Oct 25 2018
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MAPLE
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a := n -> binomial(2*n, n) - add(2^(n-m-1)*binomial(2*m, m), m = 0.. n-1);
# second program:
A029759 := n -> add((-1)^k*binomial(2*iquo(k, 2), iquo(k, 2))*binomial(n, k)*2^(n-k), k = 0 .. n): seq(A029759(n), n = 0 .. 25); # Mélika Tebni, Mar 22 2024
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MATHEMATICA
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CoefficientList[Series[(1 - 3 x) / ((1 - 2 x) Sqrt[1 - 4 x]), {x, 0, 60}], x] (* Vincenzo Librandi, Aug 25 2013 *)
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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