A168304 The fifth left hand column of triangle A167565.

24, 368, 2736, 13712, 53121, 171258, 480711, 1210572, 2793219, 5996562, 12117677, 23257104, 42696758, 75408396, 128723898, 213203256, 343741122, 540958044, 832928118, 1257300704, 1863880095, 2717733590, 3902905305, 5526820260, 7725470805

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 A167565.

Other left hand columns are A000027, A000292, A167566 and A167567.

Programs

Magma

[(321*n^9-4500*n^8+25506*n^7-75096*n^6+121905*n^5- 104580*n^4+2736*n^2+37164*n^3-3456*n)/362880: n in [5..40]]; // Vincenzo Librandi, Jul 18 2016

Mathematica

LinearRecurrence[{10,-45,120,-210,252,-210,120,-45,10,-1},{24, 368, 2736, 13712, 53121, 171258, 480711, 1210572, 2793219, 5996562},50] (* G. C. Greubel, Jul 17 2016 *)

Formula

a(n) = (321*n^9 - 4500*n^8 + 25506*n^7 - 75096*n^6 + 121905*n^5 - 104580*n^4 + 2736*n^2 + 37164*n^3 - 3456*n)/9!.

G.f.: (z^4 + 32*z^3 + 136*z^2 + 128*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) = 321.