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A089659
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a(n) = S1(n,2), where S1(n, t) = Sum_{k=0..n} (k^t * Sum_{j=0..k} binomial(n,j)).
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6
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0, 2, 19, 104, 440, 1600, 5264, 16128, 46848, 130560, 352000, 923648, 2369536, 5963776, 14766080, 36044800, 86900736, 207224832, 489357312, 1145569280, 2660761600, 6136266752, 14060355584, 32027705344, 72561459200, 163577856000, 367068708864, 820204535808
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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) = 2^(n-3)*n*(7*n^2 + 12*n + 5)/3. (see Wang and Zhang p. 333)
a(n) = 8*a(n-1) - 24*a(n-2) + 32*a(n-3) - 16*a(n-4) for n > 3.
G.f.: x*(2 + 3*x)/(1 - 2*x)^4. (End)
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MATHEMATICA
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LinearRecurrence[{8, -24, 32, -16}, {0, 2, 19, 104}, 40] (* Vincenzo Librandi, Jun 22 2016 *)
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PROG
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(Magma) I:=[0, 2, 19, 104]; [n le 4 select I[n] else 8*Self(n-1)-24*Self(n-2)+32*Self(n-3)-16*Self(n-4): n in [1..41]]; // Vincenzo Librandi, Jun 22 2016
(SageMath) [2^(n-3)*n*(7*n^2 + 12*n + 5)/3 for n in (0..40)] # G. C. Greubel, May 24 2022
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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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