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A089660
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a(n) = S1(n,3), 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, 35, 276, 1522, 6820, 26664, 94640, 312512, 975744, 2913280, 8386048, 23416320, 63724544, 169637888, 443043840, 1137934336, 2879979520, 7194083328, 17761304576, 43390730240, 104997322752, 251881062400, 599482433536, 1416470986752, 3324615065600
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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) = n*(15*n^3 + 30*n^2 + 21*n - 2)*2^(n-6). - R. J. Mathar, Sep 16 2009
G.f.: x*(2 + 15*x + 6*x^2 + 2*x^3)/(1-2*x)^5. - Maksym Voznyy (voznyy(AT)mail.ru), Jul 28 2009
a(n) = 10*a(n-1) - 40*a(n-2) + 80*a(n-3) - 80*a(n-4) + 32*a(n-5) for n > 4. - Chai Wah Wu, Jun 21 2016
E.g.f.: x*(8 + 54*x + 60*x^2 + 15*x^3)*exp(2*x)/4. - Ilya Gutkovskiy, Jun 21 2016
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MATHEMATICA
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LinearRecurrence[{10, -40, 80, -80, 32}, {0, 2, 35, 276, 1522}, 40] (* Vincenzo Librandi, Jun 22 2016 *)
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PROG
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(Magma) [2^(n-6)*n*(3*n*(7+10*n+5*n^2) -2): n in [0..40]]; // G. C. Greubel, May 24 2022
(SageMath) [n*(15*n^3+30*n^2+21*n-2)*2^(n-6) 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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