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%I #33 Mar 22 2022 09:52:23
%S 1,0,1,0,2,6,0,6,24,60,0,24,120,360,840,0,120,720,2520,6720,15120,0,
%T 720,5040,20160,60480,151200,332640,0,5040,40320,181440,604800,
%U 1663200,3991680,8648640,0,40320,362880,1814400,6652800,19958400,51891840,121080960,259459200
%N Triangle T(n,k) read by rows: T(n,k) = n! * binomial(n + k - 1, n).
%C Apart from the left column of (essentially) zeros, the same as A105725. - _R. J. Mathar_, Mar 02 2009
%D J. Riordan, An Introduction to Combinatorial Analysis, Wiley, 1958, p. 98
%H G. C. Greubel, <a href="/A156991/b156991.txt">Table of n, a(n) for the first 50 rows, flattened</a>
%F T(n, k) = RisingFactorial(n, k). - _Peter Luschny_, Mar 22 2022
%e Triangle begins as:
%e 1;
%e 0, 1;
%e 0, 2, 6;
%e 0, 6, 24, 60;
%e 0, 24, 120, 360, 840;
%e 0, 120, 720, 2520, 6720, 15120;
%e 0, 720, 5040, 20160, 60480, 151200, 332640;
%e 0, 5040, 40320, 181440, 604800, 1663200, 3991680, 8648640;
%e 0, 40320, 362880, 1814400, 6652800, 19958400, 51891840, 121080960, 259459200;
%e ...
%t Table[n!*Binomial[n+k-1, n], {n, 0, 12}, {k, 0, n}]//Flatten
%o (PARI) for(n=0,10, for(k=0,n, print1(n!*binomial(n+k-1,n), ", "))) \\ _G. C. Greubel_, Nov 19 2017
%o (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
%o (Sage)
%o for k in range(9):
%o print([rising_factorial(n, k) for n in range(k+1)])
%o # _Peter Luschny_, Mar 22 2022
%Y A092956 (row sums for n > 0).
%Y Cf. A105725.
%K nonn,tabl,easy
%O 0,5
%A _Roger L. Bagula_, Feb 20 2009
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