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 A172237 #18 Dec 26 2019 12:55:16
%S A172237 0,0,1,0,1,1,0,1,1,2,0,1,1,3,3,0,1,1,4,5,5,0,1,1,5,7,11,8,0,1,1,6,9,
%T A172237 19,21,13,0,1,1,7,11,29,40,43,21,0,1,1,8,13,41,65,97,85,34,0,1,1,9,15,
%U A172237 55,96,181,217,171,55,0,1,1,10,17,71,133,301,441,508,341,89,0,1,1,11
%N A172237 T(n,k) = T(n-1,k) + k*T(n-2,k) for k >= 1 and n >= 3 with T(0,k) = 0 and T(1,k) = T(2,k) = 1 for all k >= 1; array T(n,k), read by descending antidiagonals, with n >= 0 and k >= 1.
%C A172237 Transposed variant of A083856, without the top row of A083856.
%C A172237 Antidiagonal sums are (0, 1, 2, 4, 8, 16, 33, 70, 153, 345, ...) = (A110113(n) - 1: n >= 1).
%C A172237 Characteristic polynomials for columns are y^2 - y - k.
%e A172237 Array T(n,k) (with rows n >= 0 and columns k >= 1) begins as follows:
%e A172237 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...
%e A172237 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, ...
%e A172237 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, ...
%e A172237 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, ...
%e A172237 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, ...
%e A172237 5, 11, 19, 29, 41, 55, 71, 89, 109, 131, ...
%e A172237 8, 21, 40, 65, 96, 133, 176, 225, 280, 341, ...
%e A172237 13, 43, 97, 181, 301, 463, 673, 937, 1261, 1651, ...
%e A172237 21, 85, 217, 441, 781, 1261, 1905, 2737, 3781, 5061, ...
%e A172237 34, 171, 508, 1165, 2286, 4039, 6616, 10233, 15130, 21571, ...
%e A172237 55, 341, 1159, 2929, 6191, 11605, 19951, 32129, 49159, 72181, ...
%e A172237 ...
%p A172237 A172237 := proc(n,k)
%p A172237 if n = 0 then
%p A172237 0;
%p A172237 elif n <=2 then
%p A172237 1 ;
%p A172237 else
%p A172237 procname(n-1,k)+k*procname(n-2,k) ;
%p A172237 end if;
%p A172237 end proc: # _R. J. Mathar_, Jul 05 2012
%t A172237 f[0, a_] := 0; f[1, a_] := 1;
%t A172237 f[n_, a_] := f[n, a] = f[n - 1, a] + a*f[n - 2, a];
%t A172237 m1 = Table[f[n, a], {n, 0, 10}, {a, 1, 11}];
%t A172237 Table[Table[m1[[m, n - m + 1]], {m, 1, n}], {n, 1, 10}];
%t A172237 Flatten[%]
%Y A172237 Cf. A083856, A110113, A193376.
%K A172237 nonn,tabl,easy
%O A172237 0,10
%A A172237 _Roger L. Bagula_ and _Gary W. Adamson_, Jan 29 2010
%E A172237 More terms from _Petros Hadjicostas_, Dec 26 2019