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A167566
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The third left hand column of triangle A167565.
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4
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2, 16, 67, 202, 497, 1064, 2058, 3684, 6204, 9944, 15301, 22750, 32851, 46256, 63716, 86088, 114342, 149568, 192983, 245938, 309925, 386584, 477710, 585260, 711360, 858312, 1028601, 1224902, 1450087, 1707232, 1999624, 2330768, 2704394
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OFFSET
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3,1
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LINKS
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FORMULA
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a(n) = (7*n^5 - 30*n^4 + 45*n^3 - 30*n^2 + 8*n)/5!.
G.f.: (1*z^2 + 4*z + 2)/(1-z)^6.
a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6).
a(n) - 5*a(n-1) + 10*a(n-2) - 10*a(n-3) + 5*a(n-4) - a(n-5) = 7. (End)
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MATHEMATICA
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Table[(7*n^5 - 30*n^4 + 45*n^3 - 30*n^2 + 8*n)/5!, {n, 3, 100}] (* or *) LinearRecurrence[{6, -15, 20, -15, 6, -1}, {2, 16, 67, 202, 497, 1064}, 100] (* G. C. Greubel, Jun 16 2016 *)
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PROG
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(PARI) Vec((1*z^2 + 4*z + 2)/(1-z)^6 + O(z^50)) \\ Michel Marcus, Jul 05 2017
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CROSSREFS
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Equals the third left hand column of triangle A167565.
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KEYWORD
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easy,nonn
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AUTHOR
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STATUS
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approved
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