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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 * A046803 A280789 A121468

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 November 15 11:35 EST 2018. Contains 317238 sequences. (Running on oeis4.)