%I
%S 1,1,1,1,1,2,1,0,5,6,1,2,11,14,24,1,5,25,5,94,120,1,9,55,75,304,
%T 444,720,1,14,112,350,1099,364,3828,5040,1,20,210,1064,3969,4340,
%U 15980,25584,40320,1,27,366,2646,12873,31563,79064,34236,270576,362880
%N Triangle T(n,k) read by rows giving coefficients in expansion of n! * Sum_{i=0..n} C(x,i) in descending powers of x.
%C Apparently A190782 with reversed rows.  _Mathew Englander_, May 17 2014
%H T. D. Noe, <a href="/A054651/b054651.txt">Rows n = 0..100 of triangle, flattened</a>
%e The first few polynomials are:
%e 1, 1+x, 2+x+x^2, 6+5*x+x^3, 24+14*x+11*x^22*x^3+x^4, ...
%e So the triangle begins:
%e 1,
%e 1, 1,
%e 1, 1, 2,
%e 1, 0, 5, 6,
%e 1, 2, 11, 14, 24,
%e 1, 5, 25, 5, 94, 120,
%e 1, 9, 55, 75, 304, 444, 720,
%e 1, 14, 112, 350, 1099, 364, 3828, 5040,
%e 1, 20, 210, 1064, 3969, 4340, 15980, 25584, 40320,
%e ...
%t c[n_, k_] := Product[ni, {i, 0, k1}]/k!; row[n_] := CoefficientList[ n!*Sum[c[x, k], {k, 0, n}], x] // Reverse; Table[ row[n], {n, 0, 9}] // Flatten (* _JeanFrançois Alcover_, Oct 04 2012 *)
%Y Cf. A054649, A054655, A054654.
%K sign,tabl,nice,easy
%O 0,6
%A _N. J. A. Sloane_, Apr 17 2000
%E Missing 0 corrected by Steve Marak  _N. J. A. Sloane_, Jul 27 2012
