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A167884
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Triangle read by rows: T(n,k) 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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7
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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
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OFFSET
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1,5
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LINKS
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FORMULA
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T(n, k) = (m*n-m*k+1)*T(n-1,k-1) + (m*k-m+1)*T(n-1,k), with T(n, 1) = T(n, n) = 1, and m = 8.
Sum_{k=1..n} T(n, k) = A084948(n-1).
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EXAMPLE
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Triangle begins as:
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;
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MATHEMATICA
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T[n_, k_, m_]:= T[n, k, m]= If[k==1 || k==n, 1, (m*n-m*k+1)*T[n-1, k-1, m] + (m*k-m+1)*T[n-1, k, m]];
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PROG
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(Sage)
@CachedFunction
def T(n, k, m):
if (k==1 or k==n): return 1
else: return (m*(n-k)+1)*T(n-1, k-1, m) + (m*k-m+1)*T(n-1, k, m)
def A167884(n, k): return T(n, k, 8)
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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, A142460, A142461, A142462, A167884, ...
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KEYWORD
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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