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A094315 Triangle read by rows giving number of circular permutations of n letters such that all letters are displaced by no more than k places from their original position.

%I A094315 #14 Oct 20 2017 14:35:33
%S A094315 1,0,1,0,0,2,0,0,0,6,1,0,6,8,9,2,15,20,40,30,13,20,72,180,176,180,72,
%T A094315 20,144,609,1106,1421,980,595,154,31,1265,4960,9292,10352,8326,4096,
%U A094315 1676,304,49
%N A094315 Triangle read by rows giving number of circular permutations of n letters such that all letters are displaced by no more than k places from their original position.
%C A094315 The n-th row sums to n!.
%D A094315 J. Riordan, Discordant permutations, Scripta Math., 20 (1954), 14-23.
%H A094315 Anthony C. Robin, <a href="http://www.jstor.org/stable/40378205">90.72 Circular Wife Swapping</a>, The Mathematical Gazette, Vol. 90, No. 519 (Nov., 2006), pp. 471-478.
%H A094315 J. Riordan, <a href="/A000211/a000211.pdf">Discordant permutations</a>, Scripta Math., 20 (1954), 14-23. [Annotated scanned copy] (See Table 2)
%F A094315 Riordan (1954) is devoted to the study of these numbers and gives generating functions (involving the numbers in A061702 as coefficients).
%e A094315 1;
%e A094315 0, 1;
%e A094315 0, 0, 2;
%e A094315 0, 0, 0, 6;
%e A094315 1, 0, 6, 8, 9;
%e A094315 2, 15, 20, 40, 30, 13;
%e A094315 20, 72, 180, 176, 180, 72, 20;
%e A094315 144, 609, 1106, 1421, 980, 595, 154, 31;
%Y A094315 Diagonals give A000183 (which has further references), A000476, A000388, A000380, A000440, etc.
%Y A094315 See also A061702.
%K A094315 nonn,tabl
%O A094315 0,6
%A A094315 _N. J. A. Sloane_, based on a suggestion from _Anthony C Robin_, Jun 02 2004