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 A144637 #16 Mar 20 2022 23:14:53
%S A144637 0,0,1,-3,11,-45,175,-315,-6265,139755,-2127125,28153125,-327452125,
%T A144637 2921393475,-2998820825,-788463550875,28464750689375,-739460838241125,
%U A144637 16173782241491875,-294957734383186875,3672958879661946875,19544468129733421875,-3601613031568517590625
%N A144637 Column 2 of triangle in A144633.
%H A144637 Alois P. Heinz, <a href="/A144637/b144637.txt">Table of n, a(n) for n = 0..100</a>
%F A144637 E.g.f.: B(x)^2/2 where B(x) is e.g.f. for A144636. [_Vladeta Jovovic_, Jan 24 2009]
%p A144637 A:= proc(n, k) option remember; if n=k then 1 elif k<n or n<1 then 0 else A(n-1, k-1) +(k-1) *A(n-1, k-2) +(k-1) *(k-2) *A(n-1, k-3)/2 fi end: M:= proc(n) option remember; Matrix(n+1, (i, j)-> A(i-1, j-1))^(-1) end: a:= n-> M (n+2)[3, n+1]: seq (a(n), n=0..25); # _Alois P. Heinz_, Oct 25 2009
%t A144637 max = 22; t[n_, n_] = 1; t[n_ /; n >= 0, k_] /; (0 <= k <= 3*n) := t[n, k] = t[n-1, k-1] + (k-1)*t[n-1, k-2] + (1/2)*(k-1)*(k-2)*t[n-1, k-3]; t[_, _] = 0; A144633 = Table[t[n, k], {n, 0, max}, {k, 0, max}] // Inverse // Transpose ; A144633[[All, 3]] (* _Jean-François Alcover_, Jan 17 2014 *)
%Y A144637 Cf. A144633.
%K A144637 sign
%O A144637 0,4
%A A144637 _N. J. A. Sloane_, Jan 23 2009
%E A144637 More terms from _Alois P. Heinz_, Oct 25 2009