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 A144638 #14 Jan 17 2014 14:29:32
%S A144638 0,0,0,1,-6,35,-210,1225,-5670,-5005,750750,-16391375,278528250,
%T A144638 -4130451325,51941839950,-429736682375,-3328691115750,297526876521875,
%U A144638 -10250866397021250,276000929009430625,-6284336658393543750,114982352685697371875,-1137436827419674031250
%N A144638 Column 3 of triangle in A144633.
%H A144638 Alois P. Heinz, <a href="/A144638/b144638.txt">Table of n, a(n) for n = 0..100</a>
%F A144638 E.g.f.: B(x)^3/6 where B(x) is e.g.f. for A144636. [From _Vladeta Jovovic_, Jan 24 2009]
%p A144638 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+3)[4, n+1]: seq (a(n), n=0..25); # _Alois P. Heinz_, Oct 25 2009
%t A144638 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, 4]] (* _Jean-François Alcover_, Jan 17 2014 *)
%K A144638 sign
%O A144638 0,5
%A A144638 _N. J. A. Sloane_, Jan 23 2009
%E A144638 More terms from _Alois P. Heinz_, Oct 25 2009