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A081114
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Triangle read by rows: T(n,k) = n*T(n-1,k) + n - k starting at T(n,n)=0.
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0
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0, 1, 0, 4, 1, 0, 15, 5, 1, 0, 64, 23, 6, 1, 0, 325, 119, 33, 7, 1, 0, 1956, 719, 202, 45, 8, 1, 0, 13699, 5039, 1419, 319, 59, 9, 1, 0, 109600, 40319, 11358, 2557, 476, 75, 10, 1, 0, 986409, 362879, 102229, 23019, 4289, 679, 93, 11, 1, 0, 9864100, 3628799, 1022298, 230197, 42896, 6795, 934, 113, 12, 1, 0
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OFFSET
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0,4
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COMMENTS
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Taking the triangle into negative values of n and k would produce results close to (k+1)*e*n! - 1, i.e., one less than multiples of A000522 for nonnegative n.
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LINKS
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FORMULA
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For k > 0, T(n, k) = ceiling((A001339(k-1)/(k-1)! - (k-1)*e) *n! - 1) where A001339(k-1) = ceiling((k-1)!*(k-1)*e) for k > 1.
T(n, 0) = floor(e*n! - 1) for n > 0; T(n, 1) = n! - 1. T(n, n)=0; T(n, n-1) = n+2; T(n, n-2) = n^2 + 3*n + 5 = A027688(n+1).
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EXAMPLE
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Triangle begins
0;
1, 0;
4, 1, 0;
15, 5, 1, 0;
64, 23, 6, 1, 0;
325, 119, 33, 7, 1, 0;
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PROG
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(PARI) T(n, k) = if (k==n, 0, n*T(n-1, k) + n - k);
tabl(nn) = {for (n=0, nn, for (k=0, n, print1(T(n, k), ", "); ); print(); ); } \\ Michel Marcus, Jun 16 2019
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CROSSREFS
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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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