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A257503 Square array A(row,col) read by antidiagonals: A(1,col) = A256450(col-1), and for row > 1, A(row,col) = A255411(A(row-1,col)); Dispersion of factorial base shift A255411 (array transposed).

%I A257503 #32 Sep 20 2016 13:25:08
%S A257503 1,2,4,3,12,18,5,16,72,96,6,22,90,480,600,7,48,114,576,3600,4320,8,52,
%T A257503 360,696,4200,30240,35280,9,60,378,2880,4920,34560,282240,322560,10,
%U A257503 64,432,2976,25200,39600,317520,2903040,3265920,11,66,450,3360,25800,241920,357840,3225600,32659200,36288000,13,70,456,3456,28800,246240,2540160,3588480,35925120,399168000,439084800
%N A257503 Square array A(row,col) read by antidiagonals: A(1,col) = A256450(col-1), and for row > 1, A(row,col) = A255411(A(row-1,col)); Dispersion of factorial base shift A255411 (array transposed).
%C A257503 The array is read by antidiagonals: A(1,1), A(1,2), A(2,1), A(1,3), A(2,2), A(3,1), etc.
%C A257503 The first row (A256450) contains all the numbers which have at least one 1-digit in their factorial base representation (see A007623), after which the successive rows are obtained from the terms on the row immediately above by shifting their factorial representation one left and then incrementing the nonzero digits in that representation with a factorial base shift-operation A255411.
%H A257503 Antti Karttunen, <a href="/A257503/b257503.txt">Table of n, a(n) for n = 1..1275; the first 50 antidiagonals of array</a>
%H A257503 <a href="/index/Fa#facbase">Index entries for sequences related to factorial base representation</a>
%H A257503 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%F A257503 A(1,col) = A256450(col-1), and for row > 1, A(row,col) = A255411(A(row-1,col)).
%e A257503 The top left corner of the array:
%e A257503      1,     2,     3,     5,      6,      7,      8,      9,     10,     11,     13
%e A257503      4,    12,    16,    22,     48,     52,     60,     64,     66,     70,     76
%e A257503     18,    72,    90,   114,    360,    378,    432,    450,    456,    474,    498
%e A257503     96,   480,   576,   696,   2880,   2976,   3360,   3456,   3480,   3576,   3696
%e A257503    600,  3600,  4200,  4920,  25200,  25800,  28800,  29400,  29520,  30120,  30840
%e A257503   4320, 30240, 34560, 39600, 241920, 246240, 272160, 276480, 277200, 281520, 286560
%e A257503   ...
%o A257503 (Scheme)
%o A257503 (define (A257503 n) (A257503bi (A002260 n) (A004736 n)))
%o A257503 (define (A257503bi row col) (if (= 1 row) (A256450 (- col 1)) (A255411 (A257503bi (- row 1) col))))
%Y A257503 Transpose: A257505.
%Y A257503 Inverse permutation: A257504.
%Y A257503 Row index: A257679, Column index: A257681.
%Y A257503 Row 1: A256450, Row 2: A257692, Row 3: A257693.
%Y A257503 Columns 1-3: A001563, A062119, A130744 (without their initial zero-terms).
%Y A257503 Column 4: A213167 (without the initial one).
%Y A257503 Column 5: A052571 (without initial zeros).
%Y A257503 Cf. A007623, A256450, A255411.
%Y A257503 Cf. also permutations A255565 and A255566.
%Y A257503 Thematically similar arrays: A083412, A135764, A246278.
%K A257503 nonn,base,tabl
%O A257503 1,2
%A A257503 _Antti Karttunen_, Apr 27 2015
%E A257503 Formula changed because of the changed starting offset of A256450 - _Antti Karttunen_, May 30 2016