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Square array A(row,col) read by antidiagonals: A(1,col) = A273670(col-1), and for row > 1, A(row,col) = A153880(A(row-1,col)); Dispersion of factorial base shift A153880 (array transposed).
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%I #18 Sep 24 2016 10:49:44

%S 1,3,2,4,8,6,5,12,30,24,7,14,48,144,120,9,26,54,240,840,720,10,32,126,

%T 264,1440,5760,5040,11,36,150,744,1560,10080,45360,40320,13,38,168,

%U 864,5160,10800,80640,403200,362880,15,50,174,960,5880,41040,85680,725760,3991680,3628800,16,56,246,984,6480,46080,367920,766080,7257600,43545600,39916800

%N Square array A(row,col) read by antidiagonals: A(1,col) = A273670(col-1), and for row > 1, A(row,col) = A153880(A(row-1,col)); Dispersion of factorial base shift A153880 (array transposed).

%C The 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 Entries on row n are all multiples of n!. Dividing that factor out gives another array A276616.

%H Antti Karttunen, <a href="/A276953/b276953.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(1,col) = A273670(col-1), and for row > 1, A(row,col) = A153880(A(row-1,col))

%F As a composition of other permutations:

%F a(n) = A275848(A257503(n)).

%F Other identities. For all n >= 1:

%F A(A276949(n),A276951(n)) = n.

%e The top left corner of the array:

%e 1, 3, 4, 5, 7, 9, 10, 11, 13, 15, 16

%e 2, 8, 12, 14, 26, 32, 36, 38, 50, 56, 60

%e 6, 30, 48, 54, 126, 150, 168, 174, 246, 270, 288

%e 24, 144, 240, 264, 744, 864, 960, 984, 1464, 1584, 1680

%e 120, 840, 1440, 1560, 5160, 5880, 6480, 6600, 10200, 10920, 11520

%e 720, 5760, 10080, 10800, 41040, 46080, 50400, 51120, 81360, 86400, 90720

%o (Scheme)

%o (define (A276953 n) (A276953bi (A002260 n) (A004736 n)))

%o (define (A276953bi row col) (if (= 1 row) (A273670 (- col 1)) (A153880 (A276953bi (- row 1) col))))

%Y Inverse permutation: A276954.

%Y Transpose: A276955.

%Y Cf. A276949 (index of row where n appears), A276951 (index of column).

%Y Cf. A153880, A273670.

%Y Row 1: A273670, Row 2: A276932, Row 3: A276933.

%Y Column 1: A000142. For other columns, see the rows of transposed array A276955.

%Y Related or similar permutations: A257503, A275848, A273666.

%Y Cf. also arrays A276616, A276589 & A276943.

%K nonn,base,tabl

%O 1,2

%A _Antti Karttunen_, Sep 22 2016