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 A156991 Triangle T(n,k) read by rows: T(n,k) = n! * binomial(n + k - 1, n). 2
 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 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 COMMENTS Apart from the left column of (essentially) zeros, the same as A105725. - R. J. Mathar, Mar 02 2009 REFERENCES J. Riordan, An Introduction to Combinatorial Analysis, Wiley, 1958, p. 98 LINKS G. C. Greubel, Table of n, a(n) for the first 50 rows, flattened FORMULA T(n, k) = RisingFactorial(n, k). - Peter Luschny, Mar 22 2022 EXAMPLE 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; ... MATHEMATICA Table[n!*Binomial[n+k-1, n], {n, 0, 12}, {k, 0, n}]//Flatten PROG (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)]) # Peter Luschny, Mar 22 2022 CROSSREFS A092956 (row sums for n > 0). Cf. A105725. Sequence in context: A350256 A345208 A241810 * A229586 A294789 A197035 Adjacent sequences: A156988 A156989 A156990 * A156992 A156993 A156994 KEYWORD nonn,tabl,easy AUTHOR Roger L. Bagula, Feb 20 2009 STATUS approved

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Last modified September 22 17:32 EDT 2023. Contains 365531 sequences. (Running on oeis4.)