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A177848
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Triangle, read by rows, T(n, k) = t(k, n-k+1) - t(1, n) + 1 where t(n, m) = (n*m)!*Beta(n, m).
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1
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1, 1, 1, 1, 3, 1, 1, 55, 55, 1, 1, 1993, 12073, 1993, 1, 1, 120841, 7983241, 7983241, 120841, 1, 1, 11404081, 12454040881, 149448498481, 12454040881, 11404081, 1, 1, 1556750161, 38109367290961, 8688935743482961, 8688935743482961, 38109367290961, 1556750161, 1
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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, 5, 112, 16061, 16208166, 174379388407, 17454093335048168, 27083470639271574245769, 421762213493139881153379087370, ...}.
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LINKS
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FORMULA
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Let t(n, k) = (n*k)!*Beta(n, k) then T(n, k) = t(k, n-k+1) - t(1, n) + 1.
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EXAMPLE
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Triangle begins as:
1;
1, 1;
1, 3, 1;
1, 55, 55, 1;
1, 1993, 12073, 1993, 1;
1, 120841, 7983241, 7983241, 120841, 1;
1, 11404081, 12454040881, 149448498481, 12454040881, 11404081, 1;
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MATHEMATICA
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t[n_, k_]:= (n*k)!*Beta[n, k];
Table[t[k, n-k+1] - t[1, n] + 1, {n, 12}, {k, n}]//Flatten
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PROG
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(Sage)
def t(n, k): return factorial(n*k)*beta(n, k)
flatten([[t(k, n-k+1) - t(1, n) + 1 for k in (1..n)] for n in (1..12)]) # G. C. Greubel, Feb 06 2021
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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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