A168303 The fifth left hand column of triangle A167552.

24, 308, 2236, 11640, 47753, 163419, 485121, 1284987, 3101175, 6927921, 14502059, 28718989, 54217878, 98183330, 171418854, 289756194, 475873962, 761609034, 1190854830, 1823151902, 2738088199, 4040638965, 5867589455, 8395197525, 11848267665

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 (10,-45,120,-210,252,-210,120,-45,10,-1).

Formula

a(n) = (642*n^9 - 13833*n^8 + 132840*n^7 - 726642*n^6 + 2439738*n^5 - 5133177*n^4 + 6699660*n^3 - 5194188*n^2 + 2157840*n - 362880)/9!

G.f.: (z^5 + 53*z^4 + 260*z^3 + 236*z^2 + 68*z + 24)/(1-z)^10.

a(n) = 10*a(n-1) - 45*a(n-2) + 120*a(n-3) - 210*a(n-4) + 252*a(n-5) - 210*a(n-6) + 120*a(n-7) - 45*a(n-8) + 10*a(n-9) - a(n-10).

a(n) - 9*a(n-1) + 36*a(n-2) - 84*a(n-3) + 126*a(n-4) - 126*a(n-5) + 84*a(n-6) - 36*a(n-7) + 9*a(n-8) - a(n-9) = 2*321.

Mathematica

LinearRecurrence[{10, -45, 120, -210, 252, -210, 120, -45, 10, -1}, {24, 308, 2236, 11640, 47753, 163419, 485121, 1284987, 3101175, 6927921}, 50] (* G. C. Greubel, Jul 17 2016 *)

Prog

(Magma) [(642*n^9-13833*n^8+132840*n^7-726642*n^6+ 2439738*n^5-5133177*n^4+6699660*n^3-5194188*n^2+ 2157840*n- 362880)/362880: n in [5..40]]; // Vincenzo Librandi, Jul 18 2016

Crossrefs

Equals the fifth left hand column of triangle A167552.

Other left hand columns are A005408, A167554, A167555 and A168302.

Sequence in context: A187851 A125436 A096821 * A053215 A290939 A004413

Adjacent sequences: A168300 A168301 A168302 * A168304 A168305 A168306

Keyword

easy,nonn

Author

Johannes W. Meijer, Nov 23 2009

Status

approved