The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A368849 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A368849

Triangle read by rows: T(n, k) = binomial(n, k - 1)*(k - 1)^(k - 1)*(n - k)*(n - k + 1)^(n - k).
(history; published version)

#20 by Michael De Vlieger at Sat Jan 13 16:13:41 EST 2024

STATUS

reviewed

approved

#19 by Stefano Spezia at Sat Jan 13 15:46:17 EST 2024

STATUS

proposed

reviewed

#18 by Paolo Xausa at Sat Jan 13 15:38:13 EST 2024

STATUS

editing

proposed

#17 by Paolo Xausa at Sat Jan 13 15:30:09 EST 2024

MATHEMATICA

A368849[n_, k_] := Binomial[n, k-1] If[k == 1, 1, (k-1)^(k-1)] (n-k) (n-k+1)^(n-k);

Table[A368849[n, k], {n, 0, 10}, {k, 0, n}] (* Paolo Xausa, Jan 13 2024 *)

STATUS

approved

editing

#16 by Peter Luschny at Thu Jan 11 15:10:52 EST 2024

STATUS

editing

approved

#15 by Peter Luschny at Thu Jan 11 15:10:46 EST 2024

COMMENTS

A motivation for this triangle was to provide an alternative sum representation for A001864(n) = n! * Sum_{k=0..n-2} n^k/k!. See formula 3 and formula 15 in Riordan and Sloane.

STATUS

approved

editing

#14 by Peter Luschny at Thu Jan 11 13:38:51 EST 2024

STATUS

editing

approved

#13 by Peter Luschny at Thu Jan 11 13:38:45 EST 2024

LINKS

John Riordan and N. J. A. Sloane, <a href="http://dx.doi.org/10.1017/S1446788700007527">Enumeration of rooted trees by total height</a>, J. Austral. Math. Soc., vol. 10 pp. 278-282, 1969.

STATUS

approved

editing

#12 by Michael De Vlieger at Thu Jan 11 09:04:03 EST 2024

STATUS

proposed

approved

#11 by Peter Luschny at Thu Jan 11 08:34:46 EST 2024

STATUS

editing

proposed