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A276955 Square array A(row,col): A(row,1) = A273670(row-1), and for col > 1, A(row,col) = A153880(A(row,col-1)); Dispersion of factorial base left shift A153880.

%I A276955 #20 Sep 24 2016 16:21:34
%S A276955 1,2,3,6,8,4,24,30,12,5,120,144,48,14,7,720,840,240,54,26,9,5040,5760,
%T A276955 1440,264,126,32,10,40320,45360,10080,1560,744,150,36,11,362880,
%U A276955 403200,80640,10800,5160,864,168,38,13,3628800,3991680,725760,85680,41040,5880,960,174,50,15,39916800,43545600,7257600,766080,367920,46080,6480,984,246,56,16
%N A276955 Square array A(row,col): A(row,1) = A273670(row-1), and for col > 1, A(row,col) = A153880(A(row,col-1)); Dispersion of factorial base left shift A153880.
%C A276955 The square array A(row,col) is read by descending antidiagonals: A(1,1), A(1,2), A(2,1), A(1,3), A(2,2), A(3,1), etc.
%C A276955 When viewed in factorial base (A007623) the terms on each row start all with the same prefix, but with an increasing number of zeros appended to the end. For example, for row 8 (A001344 from a(1)=11 onward), the terms written in factorial base look as: 121, 1210, 12100, 121000, ...
%H A276955 Antti Karttunen, <a href="/A276955/b276955.txt">Table of n, a(n) for n = 1..1830; the first 60 antidiagonals of array</a>
%H A276955 <a href="/index/Fa#facbase">Index entries for sequences related to factorial base representation</a>
%H A276955 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%F A276955 A(row,1) = A273670(row-1), and for col > 1, A(row,col) = A153880(A(row,col-1))
%F A276955 As a composition of other permutations:
%F A276955 a(n) = A275848(A257505(n)).
%e A276955 The top left {1..9} x {1..18} corner of the array:
%e A276955    1,  2,   6,   24,   120,    720,    5040,    40320,    362880
%e A276955    3,  8,  30,  144,   840,   5760,   45360,   403200,   3991680
%e A276955    4, 12,  48,  240,  1440,  10080,   80640,   725760,   7257600
%e A276955    5, 14,  54,  264,  1560,  10800,   85680,   766080,   7620480
%e A276955    7, 26, 126,  744,  5160,  41040,  367920,  3669120,  40279680
%e A276955    9, 32, 150,  864,  5880,  46080,  408240,  4032000,  43908480
%e A276955   10, 36, 168,  960,  6480,  50400,  443520,  4354560,  47174400
%e A276955   11, 38, 174,  984,  6600,  51120,  448560,  4394880,  47537280
%e A276955   13, 50, 246, 1464, 10200,  81360,  730800,  7297920,  80196480
%e A276955   15, 56, 270, 1584, 10920,  86400,  771120,  7660800,  83825280
%e A276955   16, 60, 288, 1680, 11520,  90720,  806400,  7983360,  87091200
%e A276955   17, 62, 294, 1704, 11640,  91440,  811440,  8023680,  87454080
%e A276955   18, 72, 360, 2160, 15120, 120960, 1088640, 10886400, 119750400
%e A276955   19, 74, 366, 2184, 15240, 121680, 1093680, 10926720, 120113280
%e A276955   20, 78, 384, 2280, 15840, 126000, 1128960, 11249280, 123379200
%e A276955   21, 80, 390, 2304, 15960, 126720, 1134000, 11289600, 123742080
%e A276955   22, 84, 408, 2400, 16560, 131040, 1169280, 11612160, 127008000
%e A276955   23, 86, 414, 2424, 16680, 131760, 1174320, 11652480, 127370880
%o A276955 (Scheme)
%o A276955 (define (A276955 n) (A276955bi (A002260 n) (A004736 n)))
%o A276955 (define (A276955bi row col) (if (= 1 col) (A273670 (- row 1)) (A153880 (A276955bi row (- col 1)))))
%Y A276955 Inverse permutation: A276956.
%Y A276955 Transpose: A276953.
%Y A276955 Cf. A276949 (index of column where n appears), A276951 (index of row).
%Y A276955 Cf. A153880.
%Y A276955 Columns 1-3: A273670, A276932, A276933.
%Y A276955 The following lists some of the rows that have their own entries. Pattern present in the factorial base expansion of the terms on that row is given in double quotes:
%Y A276955 Row 1: A000142 (from a(1)=1, "1" onward),
%Y A276955 Row 2: A001048 (from a(2)=3, "11" onward),
%Y A276955 Row 3: A052849 (from a(2)=4, "20" onward).
%Y A276955 Row 4: A052649 (from a(1)=5, "21" onward).
%Y A276955 Row 5: A108217 (from a(3)=7, "101" onward).
%Y A276955 Row 6: A054119 (from a(3)=9, "111" onward).
%Y A276955 Row 7: A052572 (from a(2)=10, "120" onward).
%Y A276955 Row 8: A001344 (from a(1)=11, "121" onward).
%Y A276955 Row 13: A052560 (from a(3)=18, "300" onward).
%Y A276955 Row 16: A225658 (from a(1)=21, "311" onward).
%Y A276955 Row 20: A276940 (from a(3) = 27, "1011" onward).
%Y A276955 Related or similar permutations: A257505, A275848, A273666.
%Y A276955 Cf. also arrays A276617, A276588 & A276945.
%K A276955 nonn,base,tabl
%O A276955 1,2
%A A276955 _Antti Karttunen_, Sep 22 2016