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A289720
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a(n) = 1 + n*binomial(2*n,n) - n^2*(n^2 - 2*n + 3)/2.
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2
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1, 2, 7, 34, 193, 1036, 5059, 23094, 101329, 434908, 1843411, 7753582, 32441017, 135195464, 561615643, 2326740526, 9617257185, 39671268460, 163352388259, 671559953358, 2756930503801, 11303415274600, 46290177094635, 189368906606254, 773942488241473, 3160265160763176
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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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(n-1)*(69642*n - 248963)*a(n) + (-358060*n^2 + 1078397*n - 66480)*a(n-1) + 3*(56652*n^2 + 710433*n - 1732769)*a(n-2) + (749910*n^2 - 7663147*n + 14398378)*a(n-3) - 2*(157862*n - 346287)*(2*n - 7)*a(n-4) = 0.
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MAPLE
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seq(n*binomial(2*n, n)+1-n^2*(n^2-2*n+3)/2, n=0..20) ;
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PROG
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(GAP)
(PARI) a(n) = {1 + n*binomial(2*n, n) - n^2*(n^2 - 2*n + 3)/2} \\ Andrew Howroyd, Apr 26 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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EXTENSIONS
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STATUS
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approved
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