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A165678
Sixth right hand column of triangle A165674.
4
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
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.
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
KEYWORD
easy,nonn
AUTHOR
Johannes W. Meijer, Oct 05 2009
STATUS
approved

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Last modified September 20 03:37 EDT 2024. Contains 376016 sequences. (Running on oeis4.)