The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A345462

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A345462

Triangle T(n,k) (n >= 1, 0 <= k <= n-1) read by rows: number of distinct permutations after k steps of the "first transposition" algorithm.
(history; published version)

#35 by Joerg Arndt at Sun Mar 06 04:44:06 EST 2022

STATUS

reviewed

approved

#34 by Michel Marcus at Sun Mar 06 04:34:26 EST 2022

STATUS

proposed

reviewed

#33 by Jean-François Alcover at Sun Mar 06 04:20:50 EST 2022

STATUS

editing

proposed

#32 by Jean-François Alcover at Sun Mar 06 04:20:45 EST 2022

MATHEMATICA

b[n_, k_] := b[n, k] = (k+1)!*Binomial[n, k]*Sum[(-1)^i/i!, {i, 0, k+1}]/n;

T[n_, k_] := T[n, k] = If[k == 0, n!, T[n, k-1] - b[n, n-k+1]];

Table[Table[T[n, k], {k, 0, n - 1}], {n, 1, 10}] // Flatten (* Jean-François Alcover, Mar 06 2022, after Alois P. Heinz *)

STATUS

approved

editing

#31 by Alois P. Heinz at Wed Aug 11 08:54:57 EDT 2021

STATUS

editing

approved

#30 by Alois P. Heinz at Wed Aug 11 08:54:54 EDT 2021

CROSSREFS

Cf. A000142, A000166, A000255, A000274, A000313, A010027, A123513.

STATUS

approved

editing

#29 by Alois P. Heinz at Wed Aug 11 08:53:45 EDT 2021

STATUS

editing

approved

#28 by Alois P. Heinz at Wed Aug 11 08:40:57 EDT 2021

FORMULA

T(n,k) - T(n,k+1) = A123513(n,k).

CROSSREFS

Cf. A000166, A000255, A000274, A000313, A010027, A123513.

#27 by Alois P. Heinz at Wed Aug 11 08:34:31 EDT 2021

FORMULA

T(n,k) = T(n,k-1) - A010027(n,n-k) for k >= 1.

#26 by Alois P. Heinz at Wed Aug 11 08:21:00 EDT 2021

MAPLE

b:= proc(n, k) option remember; (k+1)!*

binomial(n, k)*add((-1)^i/i!, i=0..k+1)/n

end:

T:= proc(n, k) option remember;

`if`(k=0, n!, T(n, k-1)-b(n, n-k+1))

end:

seq(seq(T(n, k), k=0..n-1), n=1..10); # Alois P. Heinz, Aug 11 2021