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A168304 The fifth left hand column of triangle A167565. 4
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

5,1

LINKS

G. C. Greubel, Table of n, a(n) for n = 5..1000

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

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Last modified August 6 15:50 EDT 2020. Contains 336255 sequences. (Running on oeis4.)