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A024183
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Second elementary symmetric function of 3,4,...,n+3.
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4
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12, 47, 119, 245, 445, 742, 1162, 1734, 2490, 3465, 4697, 6227, 8099, 10360, 13060, 16252, 19992, 24339, 29355, 35105, 41657, 49082, 57454, 66850, 77350, 89037, 101997, 116319, 132095, 149420, 168392, 189112, 211684, 236215, 262815, 291597, 322677
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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) = n*(n+1)*(3*n^2 + 35*n + 106)/24.
If we define f(n,i,a) = Sum_{k=0..n-i} binomial(n,k) * Stirling1(n-k,i) * Product_{j=0..k-1} (-a-j), then a(n-2) = f(n,n-2,3), for n >= 3. - Milan Janjic, Dec 20 2008
a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5). - Colin Barker, Aug 15 2014
G.f.: -x*(4*x^2-13*x+12) / (x-1)^5. - Colin Barker, Aug 15 2014
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MAPLE
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seq(n*(n+1)*(3*n^2+35*n+106)/24, n=1..40); # Muniru A Asiru, May 19 2018
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MATHEMATICA
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f[k_] := k + 2; t[n_] := Table[f[k], {k, 1, n}]
a[n_] := SymmetricPolynomial[2, t[n]]
Table[a[n], {n, 2, 30}] (* A024183 *)
LinearRecurrence[{5, -10, 10, -5, 1}, {12, 47, 119, 245, 445}, 40] (* Vincenzo Librandi, May 03 2018 *)
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PROG
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(PARI) Vec(-x*(4*x^2-13*x+12)/(x-1)^5 + O(x^100)) \\ Colin Barker, Aug 15 2014
(Magma) [n*(n+1)*(3*n^2+35*n+106)/24: n in [1..40]]; // Vincenzo Librandi, May 03 2018
(GAP) List([1..40], n->n*(n+1)*(3*n^2+35*n+106)/24); # Muniru A Asiru, May 19 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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