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

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

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Sixth right hand column of triangle A165674.

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).

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

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.

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_Johannes W. Meijer (meijgia(AT)hotmail.com), _, Oct 05 2009

Sixth right hand column of triangle A165674

1764, 8028, 24552, 60216, 127860, 245004, 434568, 725592, 1153956, 1763100, 2604744, 3739608, 5238132, 7181196, 9660840, 12780984, 16658148, 21422172, 27216936, 34201080, 42548724, 52450188, 64112712, 77761176, 93638820

1,1

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.

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)

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

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

Cf. A165674, A007318, A028421, A126671.

easy,nonn

Johannes W. Meijer (meijgia(AT)hotmail.com), Oct 05 2009

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