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A161742
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Third left hand column of the RSEG2 triangle A161739
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5
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1, 4, 13, 30, -14, -504, 736, 44640, -104544, -10644480, 33246720, 5425056000, -20843695872, -5185511654400, 23457840537600, 8506857655296000, -44092609863966720, -22430879475779174400, 130748316971139072000
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OFFSET
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2,2
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LINKS
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FORMULA
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a(n) = sum(((-1)^k/((k+1)!*(k+2)!))*(n!)*A028246(n, k+2)*A008955(k+1, k), k=0..n-2)
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MAPLE
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nmax:=21; for n from 0 to nmax do A008955(n, 0):=1 end do: for n from 0 to nmax do A008955(n, n):=(n!)^2 end do: for n from 1 to nmax do for m from 1 to n-1 do A008955(n, m):= A008955(n-1, m-1)*n^2+A008955(n-1, m) end do: end do: for n from 1 to nmax do A028246(n, 1):=1 od: for n from 1 to nmax do A028246(n, n):=(n-1)! od: for n from 3 to nmax do for m from 2 to n-1 do A028246(n, m):=m*A028246(n-1, m)+(m-1)*A028246(n-1, m-1) od: od: for n from 2 to nmax do a(n):=sum(((-1)^k/((k+1)!*(k+2)!)) *(n!)*A028246(n, k+2)* A008955(k+1, k), k=0..n-2) od: seq(a(n), n=2..nmax);
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CROSSREFS
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Equals third left hand column of A161739 (RSEG2 triangle).
A008955 is a central factorial number triangle.
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KEYWORD
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easy,sign
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AUTHOR
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STATUS
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approved
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