OFFSET
1,3
EXAMPLE
Triangle begins:
1,
1, 3,
1, 7, 16,
1, 15, 61, 115,
1, 31, 206, 626, 1056,
1, 63, 659, 2989, 7554, 11774,
...
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 *)
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
David Applegate, Jun 19 2007
EXTENSIONS
More terms from R. J. Mathar, Aug 07 2007
STATUS
approved