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A051744
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a(n) = n*(n+1)*(n^2+5*n+18)/24.
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5
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2, 8, 21, 45, 85, 147, 238, 366, 540, 770, 1067, 1443, 1911, 2485, 3180, 4012, 4998, 6156, 7505, 9065, 10857, 12903, 15226, 17850, 20800, 24102, 27783, 31871, 36395, 41385, 46872, 52888, 59466, 66640, 74445, 82917, 92093, 102011, 112710, 124230, 136612
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OFFSET
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1,1
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LINKS
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FORMULA
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a(n) = binomial(n+3, n-1) + binomial(n+1, n-1).
a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5). - Vincenzo Librandi, Apr 27 2012
a(n) = sum_{k=1..n} sum{j=1..k} sum{i=1..j} (i + binomial(j,k)). - Wesley Ivan Hurt, Nov 01 2014
E.g.f.: (1/24)*x*(x^3+12*x^2+48*x+48)*exp(x). - Robert Israel, Nov 02 2014
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MAPLE
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MATHEMATICA
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CoefficientList[Series[(2-2*x+x^2)/(1-x)^5, {x, 0, 50}], x] (* Vincenzo Librandi, Apr 27 2012 *)
LinearRecurrence[{5, -10, 10, -5, 1}, {2, 8, 21, 45, 85}, 50] (* Harvey P. Dale, Jan 02 2024 *)
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PROG
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(Magma) I:=[2, 8, 21, 45, 85]; [n le 5 select I[n] else 5*Self(n-1)-10*Self(n-2)+10*Self(n-3)-5*Self(n-4)+Self(n-5): n in [1..50]]; // Vincenzo Librandi, Apr 27 2012
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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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Klaus Strassburger (strass(AT)ddfi.uni-duesseldorf.de), Dec 07 1999
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STATUS
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approved
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