%I A154869
%S A154869 6,26,26,230,100,230,3092,857,857,3092,53032,13671,4816,13671,53032,
%T A154869 1094774,285588,64514,64514,285588,1094774,26402826,7001142,1517286,
%U A154869 474132,1517286,7001142,26402826,728697032,195578147,43758387,8678237
%N A154869 A triangular sequence: t0(n,m) = Sum[(-1)^j*Binomial[n + 2, j]*(m - j 
               + 1)^(n + 1), {j, 0, m + 1}]; t1(n,m)=-Sum[(-1)^j*t0[n + 2, j]*(m 
               - j + 1)^(n + 1), {j, 0, m + 1}]; t(n,m)=t1(n,m)+t1(n,n-m).
%C A154869 Row sums are:
%C A154869 {6, 52, 560, 7898, 138222, 2889752, 70316640, 1953423606, 61038674510,
%C A154869 2119955154436, 81049092159048,...}
%F A154869 t0(n,m) = Sum[(-1)^j*Binomial[n + 2, j]*(m - j + 1)^(n + 1), {j, 0, m 
               + 1}]; t1(n,m)=-Sum[(-1)^j*t0[n + 2, j]*(m - j + 1)^(n + 1), {j, 
               0, m + 1}]; t(n,m)=t1(n,m)+t1(n,n-m).
%e A154869 {6},
%e A154869 {26, 26},
%e A154869 {230, 100, 230},
%e A154869 {3092, 857, 857, 3092},
%e A154869 {53032, 13671, 4816, 13671, 53032},
%e A154869 {1094774, 285588, 64514, 64514, 285588, 1094774},
%e A154869 {26402826, 7001142, 1517286, 474132, 1517286, 7001142, 26402826},
%e A154869 {728697032, 195578147, 43758387, 8678237, 8678237, 43758387, 195578147, 
               728697032},
%e A154869 {22657619468, 6133573369, 1416511360, 272313646, 78638824, 272313646, 
               1416511360, 6133573369, 22657619468},
%e A154869 {783948795698, 213534230582, 50551432780, 10112372921, 1830745237, 1830745237, 
               10112372921, 50551432780, 213534230582, 783948795698}, {29882531643406, 
               8176368342792, 1973232322854, 410347202057, 72212744396, 19707648038, 
               72212744396, 410347202057, 1973232322854, 8176368342792, 29882531643406}
%t A154869 Clear[t, t0, p, q, n, m, a, b, c];
%t A154869 t0[n_, m_] = Sum[(-1)^j*Binomial[n + 2, j]*(m - j + 1)^(n + 1), {j, 0, 
               m + 1}];
%t A154869 t[n_, m_] = -Sum[(-1)^j*t0[n + 2, j]*(m - j + 1)^(n + 1), {j, 0, m + 
               1}];
%t A154869 Table[Table[(t[n, m] + t[n, n - m]), {m, 0, n}], {n, 0, 10}];
%t A154869 Flatten[%]
%Y A154869 Sequence in context: A005938 A157025 A036175 this_sequence A043354 A023727 
               A045255
%Y A154869 Adjacent sequences: A154866 A154867 A154868 this_sequence A154870 A154871 
               A154872
%K A154869 nonn,tabl,uned,tabl
%O A154869 0,1
%A A154869 Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Jan 16 2009