0,1

Row sums are:

{2, 4, 8, 18, 73, 440, 3337, 28554, 270512, 2810718, 31841200,...}.

When divided by two this sequence is very close to Pascal's triangle,

t0(n,m)=(2 + n! - m! - (n - m)! + 2 + PartitionsP[n] - PartitionsP[ m] - PartitionsP[n - m]);

t(n,m)=(t0(n,m)+Reverse[t0(n,m)])/2

{2},

{2, 2},

{2, 4, 2},

{2, 7, 7, 2},

{2, 22, 25, 22, 2},

{2, 100, 118, 118, 100, 2},

{2, 606, 702, 717, 702, 606, 2},

{2, 4326, 4928, 5021, 5021, 4928, 4326, 2},

{2, 35289, 39611, 40210, 40288, 40210, 39611, 35289, 2},

{2, 322570, 357855, 362174, 362758, 362758, 362174, 357855, 322570, 2},

{2, 3265934, 3588500, 3623782, 3628086, 3628592, 3628086, 3623782, 3588500, 3265934, 2}

Clear[t];

t[n_, m_] =(2 + n! - m! - (n - m)! + 2 + PartitionsP[n] - PartitionsP[ m] - PartitionsP[n - m]);

Table[(Table[t[n, m], {m, 0, n}] + Reverse[Table[t[n, m], {m, 0, n}]])/2, {n, 0, 10}];

Flatten[%]

Sequence in context: A081755 A097859 A028326 this_sequence A048003 A098219 A061389

Adjacent sequences: A156043 A156044 A156045 this_sequence A156047 A156048 A156049

nonn,tabl,uned

Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Feb 02 2009