%I #6 Jun 18 2024 17:48:11

%S 1764,8028,24552,60216,127860,245004,434568,725592,1153956,1763100,

%T 2604744,3739608,5238132,7181196,9660840,12780984,16658148,21422172,

%U 27216936,34201080,42548724,52450188,64112712,77761176,93638820

%N Sixth right hand column of triangle A165674.

%C The recurrence relation leads to Pascal's triangle A007318, the a(n) formula to Wiggen's triangle A028421 and the o.g.f to Wood's polynomials A126671; see A165674.

%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (6,-15,20,-15,6,-1).

%F a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6).

%F a(n) = 120 + 548*n + 675*n^2 + 340*n^3 + 75*n^4 + 6*n^5.

%F Gf(z) = (0*z^7 - 120*z^6 + 744*z^5 - 1956*z^4 + 2844*z^3 - 2556*z^2 + 1764*z )/(z-1)^6.

%t LinearRecurrence[{6,-15,20,-15,6,-1},{1764,8028,24552,60216,127860,245004},30] (* _Harvey P. Dale_, Jun 18 2024 *)

%Y Cf. A165674, A007318, A028421, A126671.

%K easy,nonn

%O 1,1

%A _Johannes W. Meijer_, Oct 05 2009