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A327999
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a(n) = Sum_{k=0..2n}(k!*(2n - k)!)/(floor(k/2)!*floor((2n - k)/2)!)^2.
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2
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1, 5, 28, 160, 896, 4864, 25600, 131072, 655360, 3211264, 15466496, 73400320, 343932928, 1593835520, 7314866176, 33285996544, 150323855360, 674309865472, 3006477107200, 13331578486784, 58823872086016, 258385232527360, 1130297953353728, 4925812092436480
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OFFSET
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0,2
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LINKS
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FORMULA
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a(n) = 4^n*(n^2 + n + 8)/8.
a(n) = [x^n] (-16*x^2 + 7*x - 1)/(4*x - 1)^3.
a(n) = n! [x^n] exp(4*x)*(2*x^2 + x + 1).
a(n) = a(n-1)*4*(8 + n + n^2)/(8 - n + n^2).
a(n) = 12*a(n-1) - 48*a(n-2) + 64*a(n-3) for n>2.
a(n) = 2^(2*n - 3)*(8 + n + n^2).
(End)
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MATHEMATICA
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PROG
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(PARI) Vec((1 - 7*x + 16*x^2) / (1 - 4*x)^3 + O(x^25)) \\ Colin Barker, Feb 05 2020
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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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