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A167884
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Triangle read by rows: T(n,k) (1<=k<=n) given by T(n, 1) = T(n,n) = 1, otherwise T(n, k) = (m*n-m*k+1)*T(n-1,k-1)+(m*k-m+1)*T(n-1,k), where m = 8.
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2
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1, 1, 1, 1, 18, 1, 1, 179, 179, 1, 1, 1636, 6086, 1636, 1, 1, 14757, 144362, 144362, 14757, 1, 1, 132854, 2941135, 7218100, 2941135, 132854, 1, 1, 1195735, 55446309, 277509955, 277509955, 55446309, 1195735, 1, 1, 10761672, 1001178268
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OFFSET
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1,5
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COMMENTS
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Row sums are: {1, 2, 20, 360, 9360, 318240, 13366080, 668304000, 38761632000, 2558267712000,...}
The importance of this recursion is that it gives an integer inverse z transform polynomial set:
p[x_, n_] = x*Sum[a[[n, k]]*x^(k - 1), {k, 1, n}]/(x - 1)^n;
b = Table[p[x, n], {n, 0, 10}];
Table[CoefficientList[ExpandAll[InverseZTransform[b[[k]], x, n] /. UnitStep[ -1 + n] -> 1], n], {k, 1, Length[b]}]
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LINKS
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Table of n, a(n) for n=1..39.
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EXAMPLE
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{1},
{1, 1},
{1, 18, 1},
{1, 179, 179, 1},
{1, 1636, 6086, 1636, 1},
{1, 14757, 144362, 144362, 14757, 1},
{1, 132854, 2941135, 7218100, 2941135, 132854, 1},
{1, 1195735, 55446309, 277509955, 277509955, 55446309, 1195735, 1},
{1, 10761672, 1001178268, 9211047544, 18315657030, 9211047544, 1001178268, 10761672, 1},
{1, 96855113, 17633445860, 279333923732, 982069631294, 982069631294, 279333923732, 17633445860, 96855113, 1}
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MATHEMATICA
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Clear[A, p, n, k]
m = 8
A[n_, 1] := 1
A[n_, n_] := 1
A[n_, k_] := (m*n - m*k + 1)A[n - 1, k - 1] + (m*k - (m - 1))A[n - 1, k]
a = Table[A[n, k], {n, 10}, {k, n}]
Flatten[a]
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CROSSREFS
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For m = ...,-2,-1,0,1,2,3,4,5,6,7,8, ... we get ..., A225372, A144431, A007318, A008292, A060187, A142458, A142459, A142560, A142561, A142562, A167884, ...
Sequence in context: A202677 A179838 A174678 * A022181 A015144 A040332
Adjacent sequences: A167881 A167882 A167883 * A167885 A167886 A167887
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KEYWORD
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nonn,tabl
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AUTHOR
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Roger L. Bagula, Nov 14 2009
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EXTENSIONS
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Edited by N. J. A. Sloane, May 08 2013
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STATUS
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approved
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