A276616 Square array A(n,k) = A276953(n,k)/n!, 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, 3, 1, 4, 4, 1, 5, 6, 5, 1, 7, 7, 8, 6, 1, 9, 13, 9, 10, 7, 1, 10, 16, 21, 11, 12, 8, 1, 11, 18, 25, 31, 13, 14, 9, 1, 13, 19, 28, 36, 43, 15, 16, 10, 1, 15, 25, 29, 40, 49, 57, 17, 18, 11, 1, 16, 28, 41, 41, 54, 64, 73, 19, 20, 12, 1, 17, 30, 45, 61, 55, 70, 81, 91, 21, 22, 13, 1, 18, 31, 48, 66, 85, 71, 88, 100, 111, 23, 24, 14, 1

Offset: 1

Author

Antti Karttunen, Sep 22 2016

Keywords

• nonn
• base
• tabl

Examples

			The top left corner of the array:
  1, 3,  4,  5,  7,  9, 10, 11,  13,  15,  16,  17,  18,  19,  20,  21,  22
  1, 4,  6,  7, 13, 16, 18, 19,  25,  28,  30,  31,  36,  37,  39,  40,  42
  1, 5,  8,  9, 21, 25, 28, 29,  41,  45,  48,  49,  60,  61,  64,  65,  68
  1, 6, 10, 11, 31, 36, 40, 41,  61,  66,  70,  71,  90,  91,  95,  96, 100
  1, 7, 12, 13, 43, 49, 54, 55,  85,  91,  96,  97, 126, 127, 132, 133, 138
  1, 8, 14, 15, 57, 64, 70, 71, 113, 120, 126, 127, 168, 169, 175, 176, 182
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10440; the first 144 antidiagonals of array
• Index entries for sequences related to factorial base representation

Crossrefs

Transpose: A276617.

Cf. A000142, A276953.

Row 1: A273670, row 2: A276931, row 3: A276934.

For columns, see the rows of transpose A276617.

Programs

Scheme

(define (A276616 n) (A276616bi (A002260 n) (A004736 n)))
(define (A276616bi row col) (/ (A276953bi row col) (A000142 row)))

Formula

A(n,k) = A276953(n,k)/n!