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A129952
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Binomial transform of A124625.
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8
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1, 1, 2, 6, 16, 40, 96, 224, 512, 1152, 2560, 5632, 12288, 26624, 57344, 122880, 262144, 557056, 1179648, 2490368, 5242880, 11010048, 23068672, 48234496, 100663296, 209715200, 436207616, 905969664, 1879048192, 3892314112
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OFFSET
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0,3
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COMMENTS
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Number of permutations of length n>=0 avoiding the partially ordered pattern (POP) {1>2, 1>3} of length 4. That is, number of length n permutations having no subsequences of length 4 in which the first element is larger than the second and third elements. - Sergey Kitaev, Dec 08 2020
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LINKS
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FORMULA
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a(0) = 1, a(1) = 1; for n > 1, a(n) = n*2^(n-2).
G.f.: (1-3*x+2*x^2+2*x^3)/(1-2*x)^2.
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MATHEMATICA
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PROG
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(Magma) m:=15; S:=&cat[ [ 1, 2*i ]: i in [0..m] ]; [ &+[ Binomial(j-1, k-1)*S[k]: k in [1..j] ]: j in [1..2*m] ]; // Klaus Brockhaus, Jun 17 2007
(PARI) {m=29; print1(1, ", ", 1, ", "); for(n=2, m, print1(n*2^(n-2), ", "))} \\ Klaus Brockhaus, Jun 17 2007
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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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EXTENSIONS
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STATUS
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approved
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