|
%I #14 Oct 18 2017 07:01:18
%S 1,4,-2,27,-27,6,256,-384,176,-24,3125,-6250,4375,-1250,120,46656,
%T -116640,110160,-48600,9864,-720,823543,-2470629,2941225,-1764735,
%U 557032,-86436,5040,16777216,-58720256,84410368,-64225280,27725824,-6723584,836352,-40320,387420489,-1549681956
%N Triangle read by rows: T(n,k) is the coefficient of x^k of the polynomial n(n-x)(n-2x)(n-3x)...(n-(n-1)x) (n>=1, 0<=k<=n-1).
%C T(n,0) = n^n = A000312(n). Row sums yield the factorials (A000142).
%H G. C. Greubel, <a href="/A123670/b123670.txt">Table of n, a(n) for the first 50 rows, flattened</a>
%e Triangular sequence:
%e {1},
%e {4, -2},
%e {27, -27, 6},
%e {256, -384, 176, -24},
%e {3125, -6250, 4375, -1250, 120},
%e {46656, -116640, 110160, -48600,9864, -720},
%e {823543, -2470629, 2941225, -1764735, 557032, -86436, 5040},
%e {16777216, -58720256, 84410368, -64225280, 27725824, -6723584, 836352, -40320},
%e {387420489, -1549681956, 2611501074, -2410616376, 1325591001, -441450324, 86112396, -8876304, 362880},
%e {10000000000, -45000000000, 87000000000, -94500000000, 63273000000, -26932500000, 7236800000, -1172700000, 102657600, -3628800}
%p T:=(n,k)->coeff(product(n-j*x,j=0..n-1),x,k): for n from 1 to 10 do seq(T(n,k),k=0..n-1) od; # yields sequence in triangular form
%p a123670_row := proc(n) local k; seq(coeff(expand((-1)^n*n^(n-k)* pochhammer(-x,n)),x,n-k),k=0..n-1) end: # _Peter Luschny_, Nov 28 2010
%t S3[n_, x_] = Product[(n - m*x), {m, 0, n - 1}] Table[ExpandAll[S3[n, x]], {n, 0, 10}] w2 = Table[CoefficientList[S3[n, x], x], {n, 1, 10}] Flatten[w2]
%Y Cf. A048994, A008276.
%Y Cf. A000312, A000142.
%K sign,tabl
%O 1,2
%A _Gary W. Adamson_ and _Roger L. Bagula_, Nov 13 2006
%E Edited by _N. J. A. Sloane_, Nov 29 2006
|
