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A046996
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Number of Baxter permutations: A001181/2.
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4
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1, 3, 11, 46, 211, 1037, 5377, 29101, 163120, 941480, 5570280, 33664996, 207249719, 1296670793, 8229378293, 52895993341, 343891293422, 2258771535962, 14974619271658, 100117092310368, 674548712552456, 4577138309318008, 31261253291922136, 214800030086785976
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OFFSET
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2,2
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LINKS
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FORMULA
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a(n) = (1/2)*B(n, 1) where B(n, x) are the Baxter polynomials with coefficients A359363. - Peter Luschny, Jan 04 2024
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MAPLE
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a:= proc(n) option remember; `if`(n<4, 2*n-3,
((7*n^2+7*n-2)*a(n-1)+8*(n-1)*(n-2)*a(n-2))/((n+2)*(n+3)))
end:
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MATHEMATICA
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Sum[Binomial[n+1, k-1] Binomial[n+1, k] Binomial[n+1, k+1], {k, 1, n}]/(2 Binomial[n+1, 1] Binomial[n+1, 2])
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PROG
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(SageMath)
def A046996(n): return PolyA359363(n, 1) // 2
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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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