A167592 The second left hand column of triangle A167591.

-2, -8, -16, 0, 160, 896, 3584, 12288, 38400, 112640, 315392, 851968, 2236416, 5734400, 14417920, 35651584, 86900736, 209190912, 498073600, 1174405120, 2745171968, 6366953472, 14663286784, 33554432000, 76336332800, 172738215936

Offset: 2

Author

Johannes W. Meijer, Nov 10 2009

Keywords

• easy
• sign

Links

• G. C. Greubel, Table of n, a(n) for n = 2..1000
• Index entries for linear recurrences with constant coefficients, signature (8,-24,32,-16).

Crossrefs

Equals the second left hand column of triangle A167591.

Other left hand columns are A001787, A167593, A168307 and A168308.

Programs

Mathematica

LinearRecurrence[{8, -24, 32, -16}, {-2, -8, -16, 0}, 100] (* G. C. Greubel, Jun 17 2016 *)

Formula

a(n) = 2^n*(n^3 - 6*n^2 + 5*n)/12.

GF(z) = (8*z - 2)/(1-2*z)^4.

a(n) = 8*a(n-1) - 24*a(n-2) + 32*a(n-3) - 16*a(n-4).

a(n) - 7*a(n-1) + 18*a(n-2) - 20*a(n-3) + 8*a(n-4) = 1*2^(n-2).

Extensions

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