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

5,1

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) = (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.

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 *)

Prog

(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

Crossrefs

Equals the fifth left hand column of triangle A167565.

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

Sequence in context: A125481 A028074 A028111 * A053062 A028060 A026326

Adjacent sequences: A168301 A168302 A168303 * A168305 A168306 A168307

Keyword

easy,nonn

Author

Johannes W. Meijer, Nov 23 2009

Status

approved