A276617 Square array A(n,k) = A276955(n,k)/k!, read by descending antidiagonals as A(1,1), A(1,2), A(2,1), A(1,3), A(2,2), A(3,1), etc.

1, 1, 3, 1, 4, 4, 1, 5, 6, 5, 1, 6, 8, 7, 7, 1, 7, 10, 9, 13, 9, 1, 8, 12, 11, 21, 16, 10, 1, 9, 14, 13, 31, 25, 18, 11, 1, 10, 16, 15, 43, 36, 28, 19, 13, 1, 11, 18, 17, 57, 49, 40, 29, 25, 15, 1, 12, 20, 19, 73, 64, 54, 41, 41, 28, 16, 1, 13, 22, 21, 91, 81, 70, 55, 61, 45, 30, 17, 1, 14, 24, 23, 111, 100, 88, 71, 85, 66, 48, 31, 18

Offset

1,3

Links

Antti Karttunen, Table of n, a(n) for n = 1..7260; the first 120 antidiagonals of array

Index entries for sequences related to factorial base representation

Formula

A(n,k) = A276955(n,k)/k!

Example

The top left corner of the array:
1,  1,  1,  1,  1,  1,  1,   1,   1,   1,   1,   1,   1,   1,   1,   1,   1
3,  4,  5,  6,  7,  8,  9,  10,  11,  12,  13,  14,  15,  16,  17,  18,  19
4,  6,  8, 10, 12, 14, 16,  18,  20,  22,  24,  26,  28,  30,  32,  34,  36
5,  7,  9, 11, 13, 15, 17,  19,  21,  23,  25,  27,  29,  31,  33,  35,  37
7, 13, 21, 31, 43, 57, 73,  91, 111, 133, 157, 183, 211, 241, 273, 307, 343
9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225, 256, 289, 324, 361

Prog

(Scheme)
(define (A276617 n) (A276617bi (A002260 n) (A004736 n)))
(define (A276617bi row col) (/ (A276955bi row col) (A000142 col)))

Crossrefs

Transpose: A276616.

Cf. A000142, A276955.

Columns 1-3: A273670, A276931, A276934.

Row 1: A000012, Row 2: n+2, Row 3: 2n+2, Row 4: 2n+3 (for n >= 1).

Row 5: A002061 (from a(3)=7 onward).

Row 6: squares (A000290, from a(3)=9 onward).

Row 7: A028552 (from a(2)=10 onward).

Row 8: A028387 (from a(2)=11 onward).

Sequence in context: A054907 A245539 A089554 * A276616 A286623 A246340

Adjacent sequences: A276614 A276615 A276616 * A276618 A276619 A276620

Keyword

nonn,base,tabl

Author

Antti Karttunen, Sep 22 2016

Status

approved