A167567 The fourth left hand column of triangle A167565.

0, 14, 124, 601, 2120, 6096, 15168, 33858, 69432, 132990, 240812, 415987, 690352, 1106768, 1721760, 2608548, 3860496, 5595006, 7957884, 11128205, 15323704, 20806720, 27890720, 36947430, 48414600, 62804430, 80712684

Offset: 4

Author

Johannes W. Meijer, Nov 10 2009

Keywords

• easy
• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 4..1000
• Index entries for linear recurrences with constant coefficients, signature (8,-28,56,-70,56,-28,8,-1).

Crossrefs

Equals the fourth left hand column of triangle A167565.

Other left hand columns are A000027, A000292, A167566 and A168304.

Programs

Mathematica

LinearRecurrence[{8, -28, 56, -70, 56, -28, 8, -1}, {0, 14, 124, 601,
  2120, 6096, 15168, 33858}, 100] (* G. C. Greubel, Jun 16 2016 *)

Formula

a(n) = (27*n^7 - 287*n^6 + 1113*n^5 - 1925*n^4 + 1428*n^3 - 308*n^2 - 48*n)/7!.

G.f.: (1*z^3 + 12*z^2 + 14*z + 0)/(1-z)^8.

a(n) = 8*a(n-1) - 28*a(n-2) + 56*a(n-3) - 70*a(n-4) + 56*a(n-5) - 28*a(n-6) + 8*a(n-7) - a(n-8).

a(n) - 7*a(n-1) + 21*a(n-2) - 35*a(n-3) + 35*a(n-4) - 21*a(n-5) + 7*a(n-6) - a(n-7) = 27.

Extensions

Formulae and links added by Johannes W. Meijer, Nov 23 2009