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

Author

Antti Karttunen, Sep 22 2016

Keywords

• nonn
• base
• tabl

Examples

			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
		

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

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).

Programs

Scheme

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

Formula

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