The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A068106

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A068106

Euler's difference table: triangle read by rows, formed by starting with factorial numbers (A000142) and repeatedly taking differences. T(n,n) = n!, T(n,k) = T(n,k+1) - T(n-1,k).
(history; published version)

#67 by N. J. A. Sloane at Sat Aug 13 15:49:28 EDT 2022

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proposed

approved

#66 by Georg Fischer at Sat Aug 13 11:03:21 EDT 2022

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editing

proposed

#65 by Georg Fischer at Sat Aug 13 11:03:04 EDT 2022

FORMULA

D-finite recurrence for columns: T(n,k) = n*T(n-1,k) + (n-k)*T(n-2,k). - Georg Fischer, Aug 13 2022

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proposed

editing

#64 by Michel Marcus at Sat Aug 13 09:45:48 EDT 2022

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editing

proposed

#63 by Michel Marcus at Sat Aug 13 09:45:43 EDT 2022

LINKS

E. Emeric Deutsch and S. Elizalde, <a href="http://arxiv.org/abs/0904.2792">The largest and the smallest fixed points of permutations</a>, arXiv:0904.2792 [math.CO], 2009.

Philip Feinsilver, and John McSorley, <a href="https://arxiv.org/abs/1710.00788">Zeons, Permanents, the Johnson scheme, and Generalized Derangements</a>, arXiv:1710.00788 [math.CO], (2017); see page 29.

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proposed

editing

#62 by Georg Fischer at Sat Aug 13 09:39:20 EDT 2022

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editing

proposed

#61 by Georg Fischer at Sat Aug 13 09:38:01 EDT 2022

CROSSREFS

Row sums give A002467. Diagonals include A000166, A000255, A055790, A000142.

Diagonals give A000142, A001563, A001564, A001565, A001688, A001689, A023043, A023044, A023045, A023046, A023047 (factorials and k-th differences, k=1..10).

When seen as an array, main diagonal is A033815.

T(2*n, n) is A033815.

Columns k=0..10 give A000166, A000255, A055790, A277609, A277563, A280425, A280920, A284204, A284205, A284206, A284207.

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approved

editing

Discussion

Sat Aug 13

09:39

Georg Fischer: Previous text in XREFs meant the original layout as an upper right triangle.

#60 by Bruno Berselli at Fri Oct 06 08:35:08 EDT 2017

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reviewed

approved

#59 by Michel Marcus at Fri Oct 06 08:27:00 EDT 2017

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proposed

reviewed

#58 by Jon E. Schoenfield at Fri Oct 06 02:00:44 EDT 2017

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editing

proposed