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A024212
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2nd elementary symmetric function of first n+1 positive integers congruent to 1 mod 3.
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10
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4, 39, 159, 445, 1005, 1974, 3514, 5814, 9090, 13585, 19569, 27339, 37219, 49560, 64740, 83164, 105264, 131499, 162355, 198345, 240009, 287914, 342654, 404850, 475150, 554229, 642789, 741559, 851295, 972780, 1106824, 1254264, 1415964, 1592815, 1785735
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OFFSET
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1,1
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LINKS
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FORMULA
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a(n) = n*(n+1)*(9*n^2+9*n-2)/8.
a(n) = 5*a(n-1)-10*a(n-2)+10*a(n-3)-5*a(n-4)+a(n-5). - Clark Kimberling, Aug 18 2012
E.g.f.: exp(x)*x*(32+124*x+72*x^2+9*x^3)/8 = exp(x)*x*(2 + x)*(16 + 54*x + 9*x^2)/8.
a(n) = A286718(n+1, n-1), n >= 1. (End)
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MATHEMATICA
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Table[n(n+1)(9n^2+9n-2)/8, {n, 40}] (* or *) LinearRecurrence[{5, -10, 10, -5, 1}, {4, 39, 159, 445, 1005}, 40] (* Harvey P. Dale, Oct 16 2023 *)
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PROG
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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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