%I A154229
%S A154229 1,1,1,1,38,1,1,139,139,1,1,365,8828,365,1,1,807,70492,70492,807,1,1,
%T A154229 1592,357459,7062136,357459,1592,1,1,2889,1404923,98777227,98777227,
%U A154229 1404923,2889,1,1,4915,4631612,824036625,14498379854,824036625,4631612
%N A154229 A recursive triangular sequence: A(n,k)= A(n - 1, k - 1) + A(n - 1, k) 
               +(n*(n + 1)/2)^2*A(n - 2, k - 1).
%C A154229 Row sums are:
%C A154229 {1, 2, 40, 280, 9560, 142600, 7780240, 200370080, 16155726160, 638430944320,
               ...}.
%F A154229 A(n,k)= A(n - 1, k - 1) + A(n - 1, k) + (n*(n + 1)/2)^2*A(n - 2, k - 
               1).
%e A154229 {1},
%e A154229 {1, 1},
%e A154229 {1, 38, 1},
%e A154229 {1, 139, 139, 1},
%e A154229 {1, 365, 8828, 365, 1},
%e A154229 {1, 807, 70492, 70492, 807, 1},
%e A154229 {1, 1592, 357459, 7062136, 357459, 1592, 1},
%e A154229 {1, 2889, 1404923, 98777227, 98777227, 1404923, 2889, 1},
%e A154229 {1, 4915, 4631612, 824036625, 14498379854, 824036625, 4631612, 4915, 
               1},
%e A154229 {1, 7941, 13375752, 5078560312, 314123528154, 314123528154, 5078560312, 
               13375752, 7941, 1}
%t A154229 A[n_, 1] := 1; A[n_, n_] := 1;
%t A154229 A[n_, k_] := A[n - 1, k - 1] + A[n - 1, k] + (n*(n + 1)/2)^2*A[n - 2, 
               k - 1];
%t A154229 Table[Table[A[n, m], {m, 1, n}], {n, 1, 10}];
%t A154229 Flatten[%]
%Y A154229 Sequence in context: A087020 A023930 A022072 this_sequence A037936 A121672 
               A160147
%Y A154229 Adjacent sequences: A154226 A154227 A154228 this_sequence A154230 A154231 
               A154232
%K A154229 nonn,tabl,uned
%O A154229 0,5
%A A154229 Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Jan 05 2009