A168306 The fifth left hand column of triangle A167580.

105, 6534, 132444, 1593960, 13962848, 98382912, 590814336, 3137815296, 15114950400, 67240622592, 279977837568, 1102376491008, 4137416245248, 14896905748480, 51722619518976, 173913487048704, 568323403481088, 1810359422681088, 5635647921192960

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 A167580.

Other left hand columns are A014480, A167581, A167582 and A168305.

Programs

Magma

[2^n*(214*n^9-3963*n^8+30768*n^7-130536*n^6+ 330834*n^5-514332*n^4+484382*n^3-262149*n^2+72342*n- 7560)/241920: n in [5..40]]; // Vincenzo Librandi, Jul 18 2016

Mathematica

LinearRecurrence[{20,-180,960,-3360,8064,-13440,15360,-11520,5120,-1024},{105, 6534, 132444, 1593960, 13962848, 98382912, 590814336, 3137815296, 15114950400, 67240622592},50] (* G. C. Greubel, Jul 17 2016 *)

Formula

a(n) = 2^n*(214*n^9 - 3963*n^8 + 30768*n^7 - 130536*n^6 + 330834*n^5 - 514332*n^4 + 484382*n^3 - 262149*n^2 + 72342*n - 7560)/241920.

G.f.: (32*z^5 + 3728*z^4 + 20400*z^3 + 20664*z^2 + 4434*z + 105)/(2*z-1)^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-1).