A059300 Triangle of idempotent numbers binomial(n,k)*k^(n-k), version 4.

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

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