A258810 a(n) = n^9 - 1.
0, 511, 19682, 262143, 1953124, 10077695, 40353606, 134217727, 387420488, 999999999, 2357947690, 5159780351, 10604499372, 20661046783, 38443359374, 68719476735, 118587876496, 198359290367, 322687697778, 511999999999, 794280046580, 1207269217791, 1801152661462
Offset: 1
Links
- Index entries for linear recurrences with constant coefficients, signature (10,-45,120,-210,252,-210,120,-45,10,-1).
Programs
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Magma
[n^9-1: n in [1..40]];
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Magma
I:=[0,511,19682, 262143,1953124,10077695,40353606,134217727,387420488, 999999999]; [n le 10 select I[n] else 10*Self(n-1)-45*Self(n-2)+120*Self(n-3)-210*Self(n-4)+252*Self(n-5)-210*Self(n-6)+120*Self(n-7)-45*Self(n-8)+10*Self(n-9)-Self(n-10): n in [1..40]];
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Mathematica
Table[n^9 - 1, {n, 33}] (* or *) LinearRecurrence[{10, -45, 120, -210, 252, -210, 120, -45, 10, -1}, {0, 511, 19682, 262143, 1953124, 10077695, 40353606, 134217727, 387420488, 999999999}, 40]
Formula
G.f.: x^2*(511 + 14572*x + 88318*x^2 + 156064*x^3 + 88360*x^4 + 14524*x^5 + 538*x^6 - 8*x^7 + x^8)/(1-x)^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).