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Irregular table, where the n-th row consists of numbers 0..(n!-1).
5

%I #9 Feb 27 2017 09:55:31

%S 0,0,1,0,1,2,3,4,5,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,

%T 20,21,22,23,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,

%U 22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39

%N Irregular table, where the n-th row consists of numbers 0..(n!-1).

%C Used for computing A030298: a(n) tells the zero-based ranking of the n-th permutation in A030298 (A030299(n)) in the lexicographical ordering of all finite permutations of the same size.

%H A. Karttunen, <a href="/A220660/b220660.txt">The rows 1..7 of the irregular table, flattened.</a>

%F a(n) = n - A007489(A084556(n)-1) - 1.

%F a(n) = A220661(n)-1.

%e Rows of this irregular table begin as:

%e 0;

%e 0, 1;

%e 0, 1, 2, 3, 4, 5;

%t Table[Range[0,n!-1],{n,5}]//Flatten (* _Harvey P. Dale_, Feb 27 2017 *)

%o (Scheme): (define (A220660 n) (- n (A007489 (-1+ (A084556 n))) 1))

%Y Cf. A220661, A030298.

%K nonn,tabf

%O 1,6

%A _Antti Karttunen_, Dec 18 2012