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A110450
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a(n) = n*(n+1)*(n^2+n+1)/2.
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6
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0, 3, 21, 78, 210, 465, 903, 1596, 2628, 4095, 6105, 8778, 12246, 16653, 22155, 28920, 37128, 46971, 58653, 72390, 88410, 106953, 128271, 152628, 180300, 211575, 246753, 286146, 330078, 378885, 432915, 492528, 558096, 630003, 708645, 794430
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OFFSET
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0,2
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COMMENTS
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LINKS
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FORMULA
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G.f.: 3*x*(1 + x)^2/(1 - x)^5.
a(n) = Sum_{i=0..n} i*(2*i^2+1), and these are the partial sums of A061317. - Bruno Berselli, Feb 09 2017
E.g.f.: (x/2)*(6 + 15*x + 8*x^2 + x^3)*exp(x). - G. C. Greubel, Aug 24 2017
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MAPLE
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MATHEMATICA
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Table[n (n + 1) (n^2 + n + 1)/2, {n, 0, 100}] (* Wesley Ivan Hurt, Sep 27 2013 *)
CoefficientList[Series[-3 x (x^2 + 2 x + 1)/(x - 1)^5, {x, 0, 36}], x] (* or *)
LinearRecurrence[{5, -10, 10, -5, 1}, {0, 3, 21, 78, 210}, 36] (* Robert G. Wilson v, Jul 31 2018 *)
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PROG
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(GAP) List([0..40], n->n*(n+1)*(n^2+n+1)/2); # Muniru A Asiru, Aug 02 2018
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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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