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A024183
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Second elementary symmetric function of 3,4,...,n+3.
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1
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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FORMULA
| n(n+1)(3n^2+35n+106)/24.
If we define f(n,i,a)=sum(binomial(n,k)*stirling1(n-k,i)*product(-a-j,j=0..k-1),k=0..n-i), then a(n-2) = f(n,n-2,3), for n>=3. [From Milan T. Janjic (agnus(AT)blic.net), Dec 20 2008]
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MATHEMATICA
| 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 *)
(* Clark Kimberling, Dec 31 2011 *)
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CROSSREFS
| Sequence in context: A197471 A159013 A022281 * A051673 A030623 A030624
Adjacent sequences: A024180 A024181 A024182 * A024184 A024185 A024186
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KEYWORD
| nonn
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AUTHOR
| Clark Kimberling (ck6(AT)evansville.edu)
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