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

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

Crossrefs

Equals the fifth left hand column of triangle A167552.

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

Programs

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

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 *)

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.