cp's OEIS Frontend

A276953 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).

%I A276953 #18 Sep 24 2016 10:49:44
%S A276953 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 A276953 264,1440,5760,5040,11,36,150,744,1560,10080,45360,40320,13,38,168,
%U A276953 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 A276953 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 A276953 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 A276953 Entries on row n are all multiples of n!. Dividing that factor out gives another array A276616.
%H A276953 Antti Karttunen, <a href="/A276953/b276953.txt">Table of n, a(n) for n = 1..1830; the first 60 antidiagonals of array</a>
%H A276953 <a href="/index/Fa#facbase">Index entries for sequences related to factorial base representation</a>
%H A276953 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%F A276953 A(1,col) = A273670(col-1), and for row > 1, A(row,col) = A153880(A(row-1,col))
%F A276953 As a composition of other permutations:
%F A276953 a(n) = A275848(A257503(n)).
%F A276953 Other identities. For all n >= 1:
%F A276953 A(A276949(n),A276951(n)) = n.
%e A276953 The top left corner of the array:
%e A276953     1,    3,     4,     5,     7,     9,    10,    11,    13,    15,    16
%e A276953     2,    8,    12,    14,    26,    32,    36,    38,    50,    56,    60
%e A276953     6,   30,    48,    54,   126,   150,   168,   174,   246,   270,   288
%e A276953    24,  144,   240,   264,   744,   864,   960,   984,  1464,  1584,  1680
%e A276953   120,  840,  1440,  1560,  5160,  5880,  6480,  6600, 10200, 10920, 11520
%e A276953   720, 5760, 10080, 10800, 41040, 46080, 50400, 51120, 81360, 86400, 90720
%o A276953 (Scheme)
%o A276953 (define (A276953 n) (A276953bi (A002260 n) (A004736 n)))
%o A276953 (define (A276953bi row col) (if (= 1 row) (A273670 (- col 1)) (A153880 (A276953bi (- row 1) col))))
%Y A276953 Inverse permutation: A276954.
%Y A276953 Transpose: A276955.
%Y A276953 Cf. A276949 (index of row where n appears), A276951 (index of column).
%Y A276953 Cf. A153880, A273670.
%Y A276953 Row 1: A273670, Row 2: A276932, Row 3: A276933.
%Y A276953 Column 1: A000142. For other columns, see the rows of transposed array A276955.
%Y A276953 Related or similar permutations: A257503, A275848, A273666.
%Y A276953 Cf. also arrays A276616, A276589 & A276943.
%K A276953 nonn,base,tabl
%O A276953 1,2
%A A276953 _Antti Karttunen_, Sep 22 2016