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A157634
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Triangle T(n, k) = 1 if k = 0 or k = n, otherwise n^5 - k^5 - (n-k)^5, read by rows.
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1
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1, 1, 1, 1, 30, 1, 1, 210, 210, 1, 1, 780, 960, 780, 1, 1, 2100, 2850, 2850, 2100, 1, 1, 4650, 6720, 7290, 6720, 4650, 1, 1, 9030, 13650, 15540, 15540, 13650, 9030, 1, 1, 15960, 24960, 29400, 30720, 29400, 24960, 15960, 1, 1, 26280, 42210, 51030, 54900, 54900, 51030, 42210, 26280, 1
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OFFSET
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0,5
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LINKS
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FORMULA
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T(n, k) = 1 if k = 0 or k = n, otherwise 5*n*k*(n-k)*(n^2 -n*k +k^2).
T(n, n-k) = T(n, k).
Sum_{k=0..n} T(n, k) = 2 - [n=0] + 30*A006858(n).
T(2*n, n) = [n=0] + 30*A000584(n). (End)
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EXAMPLE
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Triangle begins as:
1;
1, 1;
1, 30, 1;
1, 210, 210, 1;
1, 780, 960, 780, 1;
1, 2100, 2850, 2850, 2100, 1;
1, 4650, 6720, 7290, 6720, 4650, 1;
1, 9030, 13650, 15540, 15540, 13650, 9030, 1;
1, 15960, 24960, 29400, 30720, 29400, 24960, 15960, 1;
1, 26280, 42210, 51030, 54900, 54900, 51030, 42210, 26280, 1;
1, 40950, 67200, 82950, 91200, 93750, 91200, 82950, 67200, 40950, 1;
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MATHEMATICA
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T[n_, k_]:= If[n*k*(n-k)==0, 1, n^5 - (k^5 + (n-k)^5)];
Table[T[n, k], {n, 0, 10}, {k, 0, n}]//Flatten
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PROG
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(Magma)
A157634:= func< n, k | k eq 0 or k eq n select 1 else n^5 - (k^5 + (n-k)^5) >;
(Sage)
def A157634(n, k): return 1 if (k==0 or k==n) else n^5 - (k^5 + (n-k)^5)
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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