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

Author

Johannes W. Meijer, Oct 05 2009

Keywords

• easy
• nonn

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

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

Crossrefs

Cf. A165674, A007318, A028421, A126671.

Programs

Mathematica

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

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.