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A161743
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Fourth left hand column of the RSEG2 triangle A161739.
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5
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1, 10, 73, 425, 1561, -2856, -73520, 380160, 15376416, -117209664, -7506967104, 72162155520, 7045087741056, -80246202992640, -11448278791372800, 149576169325363200, 30017051616972275712, -440857664887810867200
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OFFSET
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3,2
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LINKS
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FORMULA
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a(n) = sum(((-1)^k/((k+2)!*(k+3)!))*(n!)*A028246(n, k+3)*A008955(k+2, k), k = 0..n-3).
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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 3 to nmax do a(n) := sum(((-1)^k/((k+2)!*(k+3)!))*(n!)*A028246(n, k+3)* A008955(k+2, k), k=0..n-3) od: seq(a(n), n=3..nmax);
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CROSSREFS
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Equals fourth 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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