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A059300
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Triangle of idempotent numbers binomial(n,k)*k^(n-k), version 4.
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7
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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
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OFFSET
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0,3
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REFERENCES
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L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 91, #43 and p. 135, [3i'].
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LINKS
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G. C. Greubel, Table of n, a(n) for the first 50 rows, flattened
John Riordan and N. J. A. Sloane, Correspondence, 1974
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FORMULA
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T(n,k) = binomial(n+1,n-k+1)*(n-k+1)^k. - R. J. Mathar, Mar 14 2013
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EXAMPLE
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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;
...
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MATHEMATICA
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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 *)
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PROG
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(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
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CROSSREFS
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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
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KEYWORD
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nonn,tabl
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AUTHOR
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N. J. A. Sloane, Jan 25 2001
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STATUS
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approved
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