A168307 The fourth left hand column of triangle A167591.

-60, -768, -5008, -20672, -46720, 76800, 1540608, 10610688, 55114752, 246005760, 992808960, 3720331264, 13156941824, 44395134976, 144054681600, 452151214080, 1379061202944, 4102054477824, 11934819680256, 34047283691520, 95430020956160, 263252302888960

Offset: 4

Author

Johannes W. Meijer, Nov 23 2009, Nov 25 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 (16, -112, 448, -1120, 1792, -1792, 1024, -256).

Crossrefs

Equals the fourth left hand column of triangle A167591.

Other left hand columns are A001787, A167592, A167593 and A168308.

Programs

Magma

[2^n*(27*n^7-434*n^6+2289*n^5-5705*n^4+7938*n^3- 6461*n^2+2346*n)/10080: n in [4..30]]; // Vincenzo Librandi, Jul 18 2016

Mathematica

LinearRecurrence[{16,-112,448,-1120,1792,-1792,1024,-256}, {-60, -768, -5008, -20672, -46720, 76800, 1540608, 10610688}, 50] (* G. C. Greubel, Jul 17 2016 *)

Formula

a(n) = 2^n*(27*n^7 - 434*n^6 + 2289*n^5 - 5705*n^4 + 7938*n^3 - 6461*n^2 + 2346*n)/10080.

G.f.: (320*z^3 + 560*z^2 + 192*z - 60)/(1-2*z)^8.

a(n) = 16*a(n-1) - 112*a(n-2) + 448*a(n-3) - 1120*a(n-4) + 1792*a(n-5) - 1792*a(n-6) + 1024*a(n-7) - 256*a(n-8).

a(n) - 15*a(n-1) + 98*a(n-2) - 364*a(n-3) + 840*a(n-4) - 1232*a(n-5) + 1120*a(n-6) - 576*a(n-7) + 128*a(n-8) = 27*2^(n-2).