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%I #2 Mar 30 2012 17:34:33
%S 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,
%T 702,606,2,2,4326,4928,5021,5021,4928,4326,2,2,35289,39611,40210,
%U 40288,40210,39611,35289,2,2,322570,357855,362174,362758,362758,362174,357855
%N A triangle sequence made symmetrical by reverse coefficients: 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
%C Row sums are:
%C {2, 4, 8, 18, 73, 440, 3337, 28554, 270512, 2810718, 31841200,...}.
%C When divided by two this sequence is very close to Pascal's triangle,
%F t0(n,m)=(2 + n! - m! - (n - m)! + 2 + PartitionsP[n] - PartitionsP[ m] - PartitionsP[n - m]);
%F t(n,m)=(t0(n,m)+Reverse[t0(n,m)])/2
%e {2},
%e {2, 2},
%e {2, 4, 2},
%e {2, 7, 7, 2},
%e {2, 22, 25, 22, 2},
%e {2, 100, 118, 118, 100, 2},
%e {2, 606, 702, 717, 702, 606, 2},
%e {2, 4326, 4928, 5021, 5021, 4928, 4326, 2},
%e {2, 35289, 39611, 40210, 40288, 40210, 39611, 35289, 2},
%e {2, 322570, 357855, 362174, 362758, 362758, 362174, 357855, 322570, 2},
%e {2, 3265934, 3588500, 3623782, 3628086, 3628592, 3628086, 3623782, 3588500, 3265934, 2}
%t Clear[t];
%t t[n_, m_] =(2 + n! - m! - (n - m)! + 2 + PartitionsP[n] - PartitionsP[ m] - PartitionsP[n - m]);
%t Table[(Table[t[n, m], {m, 0, n}] + Reverse[Table[t[n, m], {m, 0, n}]])/2, {n, 0, 10}];
%t Flatten[%]
%K nonn,tabl,uned
%O 0,1
%A _Roger L. Bagula_, Feb 02 2009
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