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

5,1

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).

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).

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 *)

Prog

(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

Crossrefs

Equals the fifth left hand column of triangle A167580.

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

Sequence in context: A210138 A075350 A165055 * A075914 A075924 A359991

Adjacent sequences: A168303 A168304 A168305 * A168307 A168308 A168309

Keyword

easy,nonn

Author

Johannes W. Meijer, Nov 23 2009

Status

approved