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A001621
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a(n) = n*(n + 1)*(n^2 + n + 2)/4.
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5
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0, 2, 12, 42, 110, 240, 462, 812, 1332, 2070, 3080, 4422, 6162, 8372, 11130, 14520, 18632, 23562, 29412, 36290, 44310, 53592, 64262, 76452, 90300, 105950, 123552, 143262, 165242, 189660, 216690, 246512, 279312, 315282, 354620, 397530, 444222, 494912, 549822
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OFFSET
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0,2
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COMMENTS
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Number of integer sequences of length n+1 with sum zero and sum of absolute values 4. - R. H. Hardin, Feb 22 2009
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LINKS
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FORMULA
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G.f.: (-2*x*(x^2+x+1))/(x-1)^5. - Maksym Voznyy (voznyy(AT)mail.ru), Jul 27 2009
E.g.f.: exp(x)*x*(8 + 16*x + 8*x^2 + x^3)/4. - Stefano Spezia, Oct 08 2022
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MATHEMATICA
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Array[# (# + 1) (#^2 + # + 2)/4 &, 39, 0] (* or *)
CoefficientList[Series[-2x (x^2 + x + 1)/(x - 1)^5, {x, 0, 38}], x] (* or *)
LinearRecurrence[{5, -10, 10, -5, 1}, {0, 2, 12, 42, 110}, 39] (* Robert G. Wilson v, Aug 05 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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