A167566 The third left hand column of triangle A167565.

2, 16, 67, 202, 497, 1064, 2058, 3684, 6204, 9944, 15301, 22750, 32851, 46256, 63716, 86088, 114342, 149568, 192983, 245938, 309925, 386584, 477710, 585260, 711360, 858312, 1028601, 1224902, 1450087, 1707232, 1999624, 2330768, 2704394

Offset: 3

Author

Johannes W. Meijer, Nov 10 2009

Keywords

• easy
• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 3..1000
• Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).

Crossrefs

Equals the third left hand column of triangle A167565.

Other left hand columns are A000027, A000292, A167567 and A168304.

Programs

Mathematica

Table[(7*n^5 - 30*n^4 + 45*n^3 - 30*n^2 + 8*n)/5!, {n,3,100}] (* or *) LinearRecurrence[{6,-15,20,-15,6,-1}, {2, 16, 67, 202, 497, 1064}, 100] (* G. C. Greubel, Jun 16 2016 *)

PARI

Vec((1*z^2 + 4*z + 2)/(1-z)^6 + O(z^50)) \\ Michel Marcus, Jul 05 2017

PARI

a(n) = n*(7*n^4 - 30*n^3 + 45*n^2 - 30*n + 8)/120 \\ Charles R Greathouse IV, Jul 14 2017

Formula

From Johannes W. Meijer, Nov 23 2009: (Start)

a(n) = (7*n^5 - 30*n^4 + 45*n^3 - 30*n^2 + 8*n)/5!.

G.f.: (1*z^2 + 4*z + 2)/(1-z)^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) = 7. (End)

a(n) = A024166(n-2) + A000389(n+2). - J. M. Bergot, Jul 04 2017