The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A245692 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A245692

Number T(n,k) of endofunctions f on [n] that are self-inverse on [k] but not on [k+1]; triangle T(n,k), n>=0, 0<=k<=n, read by rows.
(history; published version)

#19 by Alois P. Heinz at Thu Dec 16 16:49:51 EST 2021

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#18 by Alois P. Heinz at Thu Dec 16 16:49:48 EST 2021

EXAMPLE

...

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#17 by Vaclav Kotesovec at Sun Feb 19 07:55:16 EST 2017

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reviewed

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#16 by Joerg Arndt at Sun Feb 19 07:29:45 EST 2017

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#15 by Jean-François Alcover at Sun Feb 19 07:20:41 EST 2017

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proposed

#14 by Jean-François Alcover at Sun Feb 19 07:20:34 EST 2017

MATHEMATICA

g[n_] := g[n] = If[n<2, 1, g[n-1] + (n-1)*g[n-2]]; H[0, 0] = 1; H[n_, k_] := Sum[Binomial[n-k, i]*Binomial[k, i]*i!*g[k-i]*n^(n-k-i), {i, 0, Min[k, n-k]}]; T[n_, k_] := H[n, k] - H[n, k+1]; Table[T[n, k], {n, 0, 10}, { k, 0, n}] // Flatten (* Jean-François Alcover, Feb 19 2017, translated from Maple *)

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#13 by Alois P. Heinz at Tue Jul 29 19:42:32 EDT 2014

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#12 by Alois P. Heinz at Tue Jul 29 19:25:30 EDT 2014

CROSSREFS

Cf. A245348, A245693 (the same for permutations).

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#11 by Alois P. Heinz at Tue Jul 29 19:03:49 EDT 2014

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#10 by Alois P. Heinz at Tue Jul 29 19:03:42 EDT 2014

EXAMPLE

T(3,1) = 7: (1,1,1), (1,1,2), (1,1,3), (1,3,1), (1,3,3), (3,1,1), (3,3,1).

T(3,2) = 4: (1,2,1), (1,2,2), (2,1,1), (2,1,2).

T(3,3) = 4: (1,2,3), (1,3,2), (2,1,3), (3,2,1).

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editing