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A024184
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Third elementary symmetric function of 3,4,...,n+4.
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1
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60, 342, 1175, 3135, 7140, 14560, 27342, 48150, 80520, 129030, 199485, 299117, 436800, 623280, 871420, 1196460, 1616292, 2151750, 2826915, 3669435, 4710860, 5986992, 7538250, 9410050, 11653200, 14324310, 17486217, 21208425, 25567560
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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FORMULA
| n(n+1)(n+2)(n+7)(n^2+13n+46)/48.
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-3,3), for n>=3. [From Milan R. Janjic (agnus(AT)blic.net), Dec 20 2008]
a(1)=60, a(2-)=342, a(3)=1175, a(4)=3135, a(5)=7140, a(6)=14560, a(7)=27342, a(n)=7*a(n-1)-21*a(n-2)+35*a(n-3)-35*a(n-4)+ 21*a(n-5)- 7*a(n-6)+a (n-7) [From Harvey P. Dale, Oct 31 2011]
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MATHEMATICA
| Table[n(n+1)(n+2)(n+7)(n^2+13n+46)/48, {n, 30}] (* or *) LinearRecurrence[ {7, -21, 35, -35, 21, -7, 1}, {60, 342, 1175, 3135, 7140, 14560, 27342}, 30] (* From Harvey P. Dale, Oct 31 2011 *)
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CROSSREFS
| Sequence in context: A033591 A133118 A092478 * A119631 A056428 A056419
Adjacent sequences: A024181 A024182 A024183 * A024185 A024186 A024187
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KEYWORD
| nonn
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AUTHOR
| Clark Kimberling (ck6(AT)evansville.edu)
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