A165678 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

Offset

1,1

Comments

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.

Links

Table of n, a(n) for n=1..25.

Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).

Formula

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.

Mathematica

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

Crossrefs

Cf. A165674, A007318, A028421, A126671.

Sequence in context: A141039 A205731 A151769 * A205912 A237781 A205904

Adjacent sequences: A165675 A165676 A165677 * A165679 A165680 A165681

Keyword

easy,nonn

Author

Johannes W. Meijer, Oct 05 2009

Status

approved