A168308 The fifth left hand column of triangle A167591.

525, 12396, 162740, 1537216, 11589216, 73898880, 413745024, 2087500800, 9672309504, 41745859584, 169680276480, 655126331392, 2419298385920, 8593269522432, 29494166618112, 98195558891520, 318148898783232, 1005877391523840, 3110695891894272

Offset: 5

Author

Johannes W. Meijer, Nov 23 2009

Keywords

• easy
• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 5..1000
• Index entries for linear recurrences with constant coefficients, signature (20, -180, 960, -3360, 8064, -13440, 15360, -11520, 5120, -1024).

Crossrefs

Equals the fifth left hand column of triangle A167591.

Other left hand columns are A001787, A167592, A167593 and A168307.

Programs

Magma

[2^n*(107*n^9-1824*n^8+14124*n^7-62538*n^6+ 165228*n^5-259476*n^4+241561*n^3-133542*n^2+ 36360*n)/241920: n in [5..30]]; // Vincenzo Librandi, Jul 18 2016

Mathematica

LinearRecurrence[{20,-180,960,-3360,8064,-13440,15360,-11520,5120,-1024},{525, 12396, 162740, 1537216, 11589216, 73898880, 413745024, 2087500800, 9672309504, 41745859584}, 50] (* G. C. Greubel, Jul 17 2016 *)

Formula

a(n) = 2^n*(107*n^9 - 1824*n^8 + 14124*n^7 - 62538*n^6 + 165228*n^5 - 259476*n^4 + 241561*n^3 - 133542*n^2 + 36360*n)/241920.

G.f.: (1936*z^4 + 9696*z^3 + 9320*z^2 + 1896*z + 525)/(1-2*z)^10.

a(n) = 20*a(n-1) - 180*a(n-2) + 960*a(n-3) - 3360*a(n-4) + 8064*a(n-5) - 13440*a(n-6) + 15360*a(n-7) - 11520*a(n-8) + 5120*a(n-9) - 1024*a(n-10).

a(n) - 19*a(n-1) + 162*a(n-2) - 816*a(n-3) + 2688*a(n-4) - 6048*a(n-5) + 9408*a(n-6) -9984*a(n-7) + 6912*a(n-8) - 2816*a(n-9) + 512*a(n-10) = 321*2^(n-2).