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A276953
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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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10
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1, 3, 2, 4, 8, 6, 5, 12, 30, 24, 7, 14, 48, 144, 120, 9, 26, 54, 240, 840, 720, 10, 32, 126, 264, 1440, 5760, 5040, 11, 36, 150, 744, 1560, 10080, 45360, 40320, 13, 38, 168, 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
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OFFSET
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1,2
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COMMENTS
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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.
Entries on row n are all multiples of n!. Dividing that factor out gives another array A276616.
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LINKS
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FORMULA
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A(1,col) = A273670(col-1), and for row > 1, A(row,col) = A153880(A(row-1,col))
As a composition of other permutations:
Other identities. For all n >= 1:
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EXAMPLE
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The top left corner of the array:
1, 3, 4, 5, 7, 9, 10, 11, 13, 15, 16
2, 8, 12, 14, 26, 32, 36, 38, 50, 56, 60
6, 30, 48, 54, 126, 150, 168, 174, 246, 270, 288
24, 144, 240, 264, 744, 864, 960, 984, 1464, 1584, 1680
120, 840, 1440, 1560, 5160, 5880, 6480, 6600, 10200, 10920, 11520
720, 5760, 10080, 10800, 41040, 46080, 50400, 51120, 81360, 86400, 90720
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PROG
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(Scheme)
(define (A276953bi row col) (if (= 1 row) (A273670 (- col 1)) (A153880 (A276953bi (- row 1) col))))
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CROSSREFS
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Cf. A276949 (index of row where n appears), A276951 (index of column).
Column 1: A000142. For other columns, see the rows of transposed array A276955.
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KEYWORD
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AUTHOR
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STATUS
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approved
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