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Square array A(row,col): A(row,1) = A256450(row-1), and for col > 1, A(row,col) = A255411(A(row,col-1)); Dispersion of factorial base shift A255411.
15

%I #31 Sep 20 2016 13:25:43

%S 1,4,2,18,12,3,96,72,16,5,600,480,90,22,6,4320,3600,576,114,48,7,

%T 35280,30240,4200,696,360,52,8,322560,282240,34560,4920,2880,378,60,9,

%U 3265920,2903040,317520,39600,25200,2976,432,64,10,36288000,32659200,3225600,357840,241920,25800,3360,450,66,11,439084800,399168000,35925120,3588480,2540160,246240,28800,3456,456,70,13

%N Square array A(row,col): A(row,1) = A256450(row-1), and for col > 1, A(row,col) = A255411(A(row,col-1)); Dispersion of factorial base shift A255411.

%C The array is read by downward antidiagonals: A(1,1), A(1,2), A(2,1), A(1,3), A(2,2), A(3,1), etc.

%C In Kimberling's terminology, this array is called the dispersion of sequence A255411 (when started from its first nonzero term, 4). The left column is the complement of that sequence, which is A256450.

%H Antti Karttunen, <a href="/A257505/b257505.txt">Table of n, a(n) for n = 1..1275; the first 50 antidiagonals of array</a>

%H Clark Kimberling, <a href="http://faculty.evansville.edu/ck6/integer/intersp.html">Interspersions and Dispersions</a>.

%H Clark Kimberling, <a href="http://www.jstor.org/discover/10.2307/2159163">Interspersions and Dispersions</a>, Proceedings of the American Mathematical Society, 117 (1993) 313-321.

%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) = A256450(row-1), and for col > 1, A(row,col) = A255411(A(row,col-1)).

%e The top left corner of the array:

%e 1, 4, 18, 96, 600, 4320, 35280, 322560, 3265920

%e 2, 12, 72, 480, 3600, 30240, 282240, 2903040, 32659200

%e 3, 16, 90, 576, 4200, 34560, 317520, 3225600, 35925120

%e 5, 22, 114, 696, 4920, 39600, 357840, 3588480, 39553920

%e 6, 48, 360, 2880, 25200, 241920, 2540160, 29030400, 359251200

%e 7, 52, 378, 2976, 25800, 246240, 2575440, 29352960, 362517120

%e 8, 60, 432, 3360, 28800, 272160, 2822400, 31933440, 391910400

%e 9, 64, 450, 3456, 29400, 276480, 2857680, 32256000, 395176320

%e 10, 66, 456, 3480, 29520, 277200, 2862720, 32296320, 395539200

%e 11, 70, 474, 3576, 30120, 281520, 2898000, 32618880, 398805120

%e 13, 76, 498, 3696, 30840, 286560, 2938320, 32981760, 402433920

%e 14, 84, 552, 4080, 33840, 312480, 3185280, 35562240, 431827200

%e 15, 88, 570, 4176, 34440, 316800, 3220560, 35884800, 435093120

%e 17, 94, 594, 4296, 35160, 321840, 3260880, 36247680, 438721920

%e 19, 100, 618, 4416, 35880, 326880, 3301200, 36610560, 442350720

%e 20, 108, 672, 4800, 38880, 352800, 3548160, 39191040, 471744000

%e 21, 112, 690, 4896, 39480, 357120, 3583440, 39513600, 475009920

%e 23, 118, 714, 5016, 40200, 362160, 3623760, 39876480, 478638720

%e ...

%o (Scheme)

%o (define (A257505 n) (A257505bi (A002260 n) (A004736 n)))

%o (define (A257505bi row col) (if (= 1 col) (A256450 (- row 1)) (A255411 (A257505bi row (- col 1)))))

%Y Transpose: A257503.

%Y Inverse permutation: A257506.

%Y Row index: A257681, Column index: A257679.

%Y Columns 1-3: A256450, A257692, A257693.

%Y Rows 1-3: A001563, A062119, A130744 (without their initial zero-terms).

%Y Row 4: A213167 (without the initial one).

%Y Row 5: A052571 (without initial zeros).

%Y Cf. A007623, A256450, A255411.

%Y Cf. also permutations A255565, A255566.

%Y Thematically similar arrays: A035513, A054582, A246279.

%K nonn,base,tabl

%O 1,2

%A _Antti Karttunen_, Apr 27 2015

%E Formula changed because of the changed starting offset of A256450 - _Antti Karttunen_, May 30 2016