This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A101845 #15 Nov 19 2024 11:47:19
%S A101845 1,1,3,1,7,16,1,15,61,115,1,31,206,626,1056,1,63,659,2989,7554,11774,
%T A101845 1,127,2052,13308,47349,105099,154624,1,255,6297,56935,274677,824331,
%U A101845 1660957,2337507,1,511,19162,237862,1518478,5960818,15747154,29428654
%N A101845 Triangle formed by left half of A101842, read by rows.
%e A101845 Triangle begins:
%e A101845 1,
%e A101845 1, 3,
%e A101845 1, 7, 16,
%e A101845 1, 15, 61, 115,
%e A101845 1, 31, 206, 626, 1056,
%e A101845 1, 63, 659, 2989, 7554, 11774,
%e A101845 ...
%p A101845 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
%t A101845 (* T is A101842 *)
%t A101845 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 A101845 T[1, -1] = T[1, 0] = 1; T[_, _] = 0;
%t A101845 A101845[n_, k_] := T[n, k-n-1];
%t A101845 Table[A101845[n, k], {n, 1, 10}, {k, 1, n}] // Flatten (* _Jean-François Alcover_, Nov 17 2024 *)
%Y A101845 Cf. A101842.
%K A101845 nonn,tabl
%O A101845 1,3
%A A101845 _David Applegate_, Jun 19 2007
%E A101845 More terms from _R. J. Mathar_, Aug 07 2007