login
A257505
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
1, 4, 2, 18, 12, 3, 96, 72, 16, 5, 600, 480, 90, 22, 6, 4320, 3600, 576, 114, 48, 7, 35280, 30240, 4200, 696, 360, 52, 8, 322560, 282240, 34560, 4920, 2880, 378, 60, 9, 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
OFFSET
1,2
COMMENTS
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.
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.
FORMULA
A(row,1) = A256450(row-1), and for col > 1, A(row,col) = A255411(A(row,col-1)).
EXAMPLE
The top left corner of the array:
1, 4, 18, 96, 600, 4320, 35280, 322560, 3265920
2, 12, 72, 480, 3600, 30240, 282240, 2903040, 32659200
3, 16, 90, 576, 4200, 34560, 317520, 3225600, 35925120
5, 22, 114, 696, 4920, 39600, 357840, 3588480, 39553920
6, 48, 360, 2880, 25200, 241920, 2540160, 29030400, 359251200
7, 52, 378, 2976, 25800, 246240, 2575440, 29352960, 362517120
8, 60, 432, 3360, 28800, 272160, 2822400, 31933440, 391910400
9, 64, 450, 3456, 29400, 276480, 2857680, 32256000, 395176320
10, 66, 456, 3480, 29520, 277200, 2862720, 32296320, 395539200
11, 70, 474, 3576, 30120, 281520, 2898000, 32618880, 398805120
13, 76, 498, 3696, 30840, 286560, 2938320, 32981760, 402433920
14, 84, 552, 4080, 33840, 312480, 3185280, 35562240, 431827200
15, 88, 570, 4176, 34440, 316800, 3220560, 35884800, 435093120
17, 94, 594, 4296, 35160, 321840, 3260880, 36247680, 438721920
19, 100, 618, 4416, 35880, 326880, 3301200, 36610560, 442350720
20, 108, 672, 4800, 38880, 352800, 3548160, 39191040, 471744000
21, 112, 690, 4896, 39480, 357120, 3583440, 39513600, 475009920
23, 118, 714, 5016, 40200, 362160, 3623760, 39876480, 478638720
...
PROG
(Scheme)
(define (A257505 n) (A257505bi (A002260 n) (A004736 n)))
(define (A257505bi row col) (if (= 1 col) (A256450 (- row 1)) (A255411 (A257505bi row (- col 1)))))
CROSSREFS
Transpose: A257503.
Inverse permutation: A257506.
Row index: A257681, Column index: A257679.
Columns 1-3: A256450, A257692, A257693.
Rows 1-3: A001563, A062119, A130744 (without their initial zero-terms).
Row 4: A213167 (without the initial one).
Row 5: A052571 (without initial zeros).
Cf. also permutations A255565, A255566.
Thematically similar arrays: A035513, A054582, A246279.
Sequence in context: A302461 A303243 A074676 * A152883 A285793 A117692
KEYWORD
nonn,base,tabl
AUTHOR
Antti Karttunen, Apr 27 2015
EXTENSIONS
Formula changed because of the changed starting offset of A256450 - Antti Karttunen, May 30 2016
STATUS
approved