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 A054651 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. 11
 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, 444, 720, 1, -14, 112, -350, 1099, 364, 3828, 5040, 1, -20, 210, -1064, 3969, -4340, 15980, 25584, 40320, 1, -27, 366, -2646, 12873, -31563, 79064, 34236, 270576, 362880 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,6 COMMENTS Apparently A190782 with reversed rows. - Mathew Englander, May 17 2014 LINKS T. D. Noe, Rows n = 0..100 of triangle, flattened EXAMPLE The first few polynomials are: 1, 1+x, 2+x+x^2, 6+5*x+x^3, 24+14*x+11*x^2-2*x^3+x^4, ... So the triangle begins: 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, 444, 720; 1, -14, 112, -350, 1099, 364, 3828, 5040; 1, -20, 210, -1064, 3969, -4340, 15980, 25584, 40320; ... MATHEMATICA c[n_, k_] := Product[n-i, {i, 0, k-1}]/k!; row[n_] := CoefficientList[ n!*Sum[c[x, k], {k, 0, n}], x] // Reverse; Table[ row[n], {n, 0, 9}] // Flatten (* Jean-François Alcover, Oct 04 2012 *) CROSSREFS T(2*n,n) gives A347987. Cf. A054649, A054655, A054654. Sequence in context: A176056 A298213 A130191 * A292323 A059720 A140589 Adjacent sequences: A054648 A054649 A054650 * A054652 A054653 A054654 KEYWORD sign,tabl,nice,easy AUTHOR N. J. A. Sloane, Apr 17 2000 EXTENSIONS Missing 0 corrected by Steve Marak - N. J. A. Sloane, Jul 27 2012 STATUS approved

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Last modified April 12 14:01 EDT 2024. Contains 371635 sequences. (Running on oeis4.)