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Triangle read by rows: T(n,m)=A060187(1+n,1+m) *n! / (n-m)!
1

%I #5 Jun 17 2015 04:14:11

%S 1,1,1,1,12,2,1,69,138,6,1,304,2760,1824,24,1,1185,33640,100920,28440,

%T 120,1,4332,316290,2825760,3795480,519840,720,1,15253,2547594,

%U 54541830,218167320,152855640,10982160,5040,1,52416,18570272,835056768

%N Triangle read by rows: T(n,m)=A060187(1+n,1+m) *n! / (n-m)!

%C Row sums are: 1, 2, 15, 214, 4913, 164306, 7462423, 439114838, 32358353217, 2909210035042, 312597121198751,...

%e 1;

%e 1, 1;

%e 1, 12, 2;

%e 1, 69, 138, 6;

%e 1, 304, 2760, 1824, 24;

%e 1, 1185, 33640, 100920, 28440, 120;

%e 1, 4332, 316290, 2825760, 3795480, 519840, 720;

%e 1, 15253, 2547594, 54541830, 218167320, 152855640, 10982160, 5040;

%e 1, 52416, 18570272, 835056768, 7854023520, 16701135360, 6685297920, 264176640, 40320;

%e 1, 177057, 126456480, 10940817888, 209905801056, 1049529005280, 1312898146560, 318670329600, 7138938240, 362880;

%p A177429 := proc(n,k)

%p A060187(n+1,k+1)*n!/(n-k)! ;

%p end proc: # _R. J. Mathar_, Jun 16 2015

%t (*A060187*);

%t p[x_, n_] = (1 - x)^(n + 1)*Sum[(2*k + 1)^n*x^k, {k, 0, Infinity}];

%t f[n_, m_] := CoefficientList[FullSimplify[ExpandAll[p[x, n]]], x][[m + 1]];

%t t[n_, m_] := f[n, m]*n!/(n - m)!;

%t Table[Table[t[n, m], {m, 0, n}], {n, 0, 10}];

%t Flatten[%]

%Y Cf. A060187

%K nonn,tabl,easy

%O 0,5

%A _Roger L. Bagula_, May 08 2010