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