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A156991
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Triangle T(n,k) read by rows: T(n,k) = n! * binomial(n + k - 1, n).
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2
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1, 0, 1, 0, 2, 6, 0, 6, 24, 60, 0, 24, 120, 360, 840, 0, 120, 720, 2520, 6720, 15120, 0, 720, 5040, 20160, 60480, 151200, 332640, 0, 5040, 40320, 181440, 604800, 1663200, 3991680, 8648640, 0, 40320, 362880, 1814400, 6652800, 19958400, 51891840, 121080960, 259459200
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OFFSET
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0,5
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COMMENTS
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Apart from the left column of (essentially) zeros, the same as A105725. - R. J. Mathar, Mar 02 2009
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REFERENCES
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J. Riordan, An Introduction to Combinatorial Analysis, Wiley, 1958, p. 98
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LINKS
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FORMULA
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EXAMPLE
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Triangle begins as:
1;
0, 1;
0, 2, 6;
0, 6, 24, 60;
0, 24, 120, 360, 840;
0, 120, 720, 2520, 6720, 15120;
0, 720, 5040, 20160, 60480, 151200, 332640;
0, 5040, 40320, 181440, 604800, 1663200, 3991680, 8648640;
0, 40320, 362880, 1814400, 6652800, 19958400, 51891840, 121080960, 259459200;
...
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MATHEMATICA
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Table[n!*Binomial[n+k-1, n], {n, 0, 12}, {k, 0, n}]//Flatten
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PROG
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(PARI) for(n=0, 10, for(k=0, n, print1(n!*binomial(n+k-1, n), ", "))) \\ G. C. Greubel, Nov 19 2017
(Sage) flatten([[factorial(n)*binomial(n+k-1, n) for k in (0..n)] for n in (0..12)]) # G. C. Greubel, May 10 2021
(Sage)
for k in range(9):
print([rising_factorial(n, k) for n in range(k+1)])
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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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