A017229 a(n) = (9*n + 5)^9.

1953125, 20661046784, 1801152661463, 35184372088832, 327381934393961, 1953125000000000, 8662995818654939, 31087100296429568, 95151694449171437, 257327417311663616, 630249409724609375, 1423311812421484544

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..10000
• Index entries for linear recurrences with constant coefficients, signature (10, -45, 120, -210, 252, -210, 120, -45, 10, -1).

Programs

Magma

[(9*n+5)^9: n in [0..20]]; // Vincenzo Librandi, Jul 24 2011

Mathematica

(9*Range[0,20]+5)^9 (* or *) LinearRecurrence[{10,-45,120,-210,252,-210,120,-45,10,-1},{1953125,20661046784,1801152661463,35184372088832,327381934393961,1953125000000000,8662995818654939,31087100296429568,95151694449171437,257327417311663616}, 20] (* Harvey P. Dale, Mar 26 2013 *)

Formula

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(0)=1953125, a(1)=20661046784, a(2)=1801152661463, a(3)=35184372088832, a(4)=327381934393961, a(5)=1953125000000000, a(6)=8662995818654939, a(7)=31087100296429568, a(8)=95151694449171437, a(9)=257327417311663616. - Harvey P. Dale, Mar 26 2013