A101845 Triangle formed by left half of A101842, read by rows.

1, 1, 3, 1, 7, 16, 1, 15, 61, 115, 1, 31, 206, 626, 1056, 1, 63, 659, 2989, 7554, 11774, 1, 127, 2052, 13308, 47349, 105099, 154624, 1, 255, 6297, 56935, 274677, 824331, 1660957, 2337507, 1, 511, 19162, 237862, 1518478, 5960818, 15747154, 29428654

Offset: 1

Author

David Applegate, Jun 19 2007

Keywords

• nonn
• tabl

Examples

			Triangle begins:
  1,
  1,  3,
  1,  7,  16,
  1, 15,  61,  115,
  1, 31, 206,  626, 1056,
  1, 63, 659, 2989, 7554, 11774,
  ...
		

Crossrefs

Cf. A101842.

Programs

Maple

A101842 := proc(n,k) option remember ; if k < -n or k >= n then 0 ; elif n = 1 then 1; else (n-k)*A101842(n-1,k-1)+A101842(n-1,k)+(n+k+1)*A101842(n-1,k+1) ; fi ; end: A101845 := proc(n,k) A101842(n,-n+k-1) ; end: for n from 1 to 10 do for k from 1 to n do printf("%d, ",A101845(n,k)) ; od: od: # R. J. Mathar, Aug 07 2007

Mathematica

(* T is A101842 *)
T[n_, k_] /; -n <= k <= n-1 := T[n, k] = (n-k)*T[n-1, k-1]+T[n-1, k]+(n+k+1)* T[n-1, k+1];
T[1, -1] = T[1, 0] = 1; T[, ] = 0;
A101845[n_, k_] := T[n, k-n-1];
Table[A101845[n, k], {n, 1, 10}, {k, 1, n}] // Flatten (* Jean-François Alcover, Nov 17 2024 *)

Extensions

More terms from R. J. Mathar, Aug 07 2007