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 A059300 Triangle of idempotent numbers binomial(n,k)*k^(n-k), version 4. 7
 1, 1, 2, 1, 6, 3, 1, 12, 24, 4, 1, 20, 90, 80, 5, 1, 30, 240, 540, 240, 6, 1, 42, 525, 2240, 2835, 672, 7, 1, 56, 1008, 7000, 17920, 13608, 1792, 8, 1, 72, 1764, 18144, 78750, 129024, 61236, 4608, 9, 1, 90, 2880, 41160, 272160, 787500, 860160, 262440, 11520, 10 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 REFERENCES L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 91, #43 and p. 135, [3i']. LINKS G. C. Greubel, Table of n, a(n) for the first 50 rows, flattened John Riordan and N. J. A. Sloane, Correspondence, 1974 FORMULA T(n,k) = binomial(n+1,n-k+1)*(n-k+1)^k. - R. J. Mathar, Mar 14 2013 EXAMPLE Triangle begins: 1; 1, 2; 1, 6, 3; 1, 12, 24, 4; 1, 20, 90, 80, 5; 1, 30, 240, 540, 240, 6; 1, 42, 525, 2240, 2835, 672, 7; ... MATHEMATICA t[n_, k_] := Binomial[n + 1, k]*(n - k + 1)^k; Flatten@Table[t[n, k], {n, 0, 9}, {k, 0, n}] (* Arkadiusz Wesolowski, Mar 23 2013 *) PROG (Magma) /* As triangle: */ [[Binomial(n+1, n-k+1)*(n-k+1)^k: k in [0..n]]: n in [0.. 15]]; // Vincenzo Librandi, Aug 22 2015 (PARI) for(n=0, 25, for(k=0, n, print1(binomial(n+1, k)*(n-k+1)^k, ", "))) \\ G. C. Greubel, Jan 05 2017 CROSSREFS There are 4 versions: A059297-A059300. Diagonals give A001788, A036216, A040075, A050982, A002378, 3*A002417, etc. Row sums are A000248. Sequence in context: A222969 A132813 A034898 * A321331 A046803 A280789 Adjacent sequences: A059297 A059298 A059299 * A059301 A059302 A059303 KEYWORD nonn,tabl AUTHOR N. J. A. Sloane, Jan 25 2001 STATUS approved

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Last modified March 27 13:50 EDT 2023. Contains 361572 sequences. (Running on oeis4.)