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%I #2 Mar 30 2012 17:34:39
%S 1,1,1,1,31,1,1,721,721,1,1,16201,104521,16201,1,1,389761,10944361,
%T 10944361,389761,1,1,10367281,1021305601,4202679601,1021305601,
%U 10367281,1,1,307480321,92886433921,1229523926401,1229523926401,92886433921
%N A symmetrical triangle sequence: t(n,m)=n!*Eulerian[n + 1, m]^2 - n! + 1
%C Row sums are:
%C {1, 2, 33, 1444, 136925, 22668246, 6266025367, 2645435681288,
%C 1628649184821129, 1398189017071123210, 1620879822232935264011,...}.
%F t(n,m)=n!*Eulerian[n + 1, m]^2 - n! + 1
%e {1},
%e {1, 1},
%e {1, 31, 1},
%e {1, 721, 721, 1},
%e {1, 16201, 104521, 16201, 1},
%e {1, 389761, 10944361, 10944361, 389761, 1},
%e {1, 10367281, 1021305601, 4202679601, 1021305601, 10367281, 1},
%e {1, 307480321, 92886433921, 1229523926401, 1229523926401, 92886433921, 307480321, 1},
%e {1, 10160760961, 8604032492161, 313900826601601, 983619145111681, 313900826601601, 8604032492161, 10160760961, 1},
%e {1, 372375843841, 830510972565121, 75188647770445441, 623074977416707201, 623074977416707201, 75188647770445441, 830510972565121, 372375843841, 1},
%e {1, 15042446496001, 84543977513318401, 17619128067859718401, 344122240288359456001, 897227967480577286401, 344122240288359456001, 17619128067859718401, 84543977513318401, 15042446496001, 1}
%t << DiscreteMath`Combinatorica`
%t t[n_, m_] = n!*Eulerian[n + 1, m]^2 - n! + 1;
%t Table[Table[t[n, m], {m, 0, n}], {n, 0, 10}];
%t Flatten[%]
%K nonn,tabl,uned
%O 0,5
%A _Roger L. Bagula_, Mar 27 2010
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