0,1

Row sums are:

{6, 52, 560, 7898, 138222, 2889752, 70316640, 1953423606, 61038674510,

2119955154436, 81049092159048,...}

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).

{6},

{26, 26},

{230, 100, 230},

{3092, 857, 857, 3092},

{53032, 13671, 4816, 13671, 53032},

{1094774, 285588, 64514, 64514, 285588, 1094774},

{26402826, 7001142, 1517286, 474132, 1517286, 7001142, 26402826},

{728697032, 195578147, 43758387, 8678237, 8678237, 43758387, 195578147, 728697032},

{22657619468, 6133573369, 1416511360, 272313646, 78638824, 272313646, 1416511360, 6133573369, 22657619468},

{783948795698, 213534230582, 50551432780, 10112372921, 1830745237, 1830745237, 10112372921, 50551432780, 213534230582, 783948795698}, {29882531643406, 8176368342792, 1973232322854, 410347202057, 72212744396, 19707648038, 72212744396, 410347202057, 1973232322854, 8176368342792, 29882531643406}

Clear[t, t0, p, q, n, m, a, b, c];

t0[n_, m_] = Sum[(-1)^j*Binomial[n + 2, j]*(m - j + 1)^(n + 1), {j, 0, m + 1}];

t[n_, m_] = -Sum[(-1)^j*t0[n + 2, j]*(m - j + 1)^(n + 1), {j, 0, m + 1}];

Table[Table[(t[n, m] + t[n, n - m]), {m, 0, n}], {n, 0, 10}];

Flatten[%]

Sequence in context: A005938 A157025 A036175 this_sequence A043354 A023727 A045255

Adjacent sequences: A154866 A154867 A154868 this_sequence A154870 A154871 A154872

nonn,tabl,uned,tabl

Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Jan 16 2009