A168302 The fourth left hand column of triangle A167552.

-8, -66, -264, -689, -1255, -1360, 684, 8502, 28842, 73150, 159588, 315549, 580723, 1010768, 1681640, 2694636, 4182204, 6314574, 9307264, 13429515, 19013709, 26465824, 36276980, 49036130, 65443950, 86327982, 112659084

Offset: 4

Author

Johannes W. Meijer, Nov 23 2009

Keywords

• easy
• sign

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 A167552.

Other left hand columns are A005408, A167554, A167555 and A168303.

Programs

Mathematica

LinearRecurrence[{8,-28,56,-70,56,-28,8,-1},{-8, -66, -264, -689, -1255, -1360, 684, 8502},50] (* G. C. Greubel, Jul 17 2016 *)

Formula

a(n) = (54*n^7 - 1057*n^6 + 7245*n^5 - 24535*n^4 + 45801*n^3 - 47488*n^2 + 25020*n - 5040)/7!.

G.f.: (z^4 + 23*z^3 + 40*z^2 - 2*z - 8)/(z-1)^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) = 2*27.