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 A054649 Triangle T(n,k) giving coefficients in expansion of k! * Sum_{i=0..k} C(x-k,i) in powers of x. 1
 1, 1, 0, 1, -3, 4, 1, -9, 32, -36, 1, -18, 131, -426, 528, 1, -30, 375, -2370, 7544, -9600, 1, -45, 865, -8955, 52414, -163800, 213120, 1, -63, 1729, -26565, 245854, -1366932, 4220376, -5574240, 1, -84, 3122, -66696, 893249, -7664916 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 LINKS EXAMPLE For k=2 we get 1+C(x-2,1)+C(x-2,2) = x^2-3x+4. 1; 1,0; 1,-3,4; 1,-9,32,-36; ... MATHEMATICA c[n_, k_] := Product[n-i, {i, 0, k-1}]/k!; row[n_] := CoefficientList[ n!*Sum[c[x-n, k], {k, 0, n}], x] // Reverse; Table[ row[n], {n, 0, 8}] // Flatten  (* Jean-François Alcover, Oct 04 2012 *) CROSSREFS Cf. A054651, A008275, A008276, A048994. Sequence in context: A164948 A102051 A078068 * A138263 A147721 A172094 Adjacent sequences:  A054646 A054647 A054648 * A054650 A054651 A054652 KEYWORD sign,tabl,nice AUTHOR N. J. A. Sloane, Apr 16 2000 STATUS approved

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Last modified June 21 18:50 EDT 2021. Contains 345365 sequences. (Running on oeis4.)