%I #14 Sep 24 2016 10:47:35

%S 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,

%T 14,13,31,25,18,11,1,10,16,15,43,36,28,19,13,1,11,18,17,57,49,40,29,

%U 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

%N 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.

%H Antti Karttunen, <a href="/A276617/b276617.txt">Table of n, a(n) for n = 1..7260; the first 120 antidiagonals of array</a>

%H <a href="/index/Fa#facbase">Index entries for sequences related to factorial base representation</a>

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

%e The top left corner of the array:

%e 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1

%e 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19

%e 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36

%e 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37

%e 7, 13, 21, 31, 43, 57, 73, 91, 111, 133, 157, 183, 211, 241, 273, 307, 343

%e 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225, 256, 289, 324, 361

%o (Scheme)

%o (define (A276617 n) (A276617bi (A002260 n) (A004736 n)))

%o (define (A276617bi row col) (/ (A276955bi row col) (A000142 col)))

%Y Transpose: A276616.

%Y Cf. A000142, A276955.

%Y Columns 1-3: A273670, A276931, A276934.

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

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

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

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

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

%K nonn,base,tabl

%O 1,3

%A _Antti Karttunen_, Sep 22 2016