A167555 The third left hand column of triangle A167552.

2, 14, 63, 209, 559, 1281, 2618, 4902, 8568, 14168, 22385, 34047, 50141, 71827, 100452, 137564, 184926, 244530, 318611, 409661, 520443, 654005, 813694, 1003170, 1226420, 1487772, 1791909, 2143883, 2549129, 3013479, 3543176

Offset: 3

Author

Johannes W. Meijer, Nov 10 2009

Keywords

• easy
• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 3..1002
• Index entries for linear recurrences with constant coefficients, signature (6, -15, 20, -15, 6, -1).

Crossrefs

Equals the third left hand column of triangle A167552.

Other left hand columns are A005408, A167554, A168302 and A168303.

Programs

Mathematica

LinearRecurrence[{6,-15,20,-15,6,-1},{2,14,63,209,559,1281},40] (* or *) Table[1/120*(66*n+95*n^2+40*n^3+25*n^4+14*n^5),{n,40}] (* Harvey P. Dale, Mar 26 2012 *)

Formula

a(n) = (14*n^5 - 115*n^4 + 400*n^3 - 665*n^2 + 486*n - 120)/5!.

G.f.: (z^3 + 9*z^2 + 2*z + 2)/(z-1)^6.

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) - 5*a(n-1) + 10*a(n-2) - 10*a(n-3) + 5*a(n-4) - a(n-5) = 2*7.