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A258809
a(n) = n^8 - 1.
1
0, 255, 6560, 65535, 390624, 1679615, 5764800, 16777215, 43046720, 99999999, 214358880, 429981695, 815730720, 1475789055, 2562890624, 4294967295, 6975757440, 11019960575, 16983563040, 25599999999, 37822859360, 54875873535, 78310985280, 110075314175
OFFSET
1,2
FORMULA
G.f.: x^2*(225 + 4535*x + 14595*x^2 + 18069*x^3 + 569*x^4 + 3999*x^5 - 2511*x^6 + 1079*x^7 - 270*x^8 + 30*x^9) / (1 - x)^9.
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).
a(n) = (n - 1)*(n + 1)*(n^2 + 1)*(n^4 + 1) = -A024006(n). [Bruno Berselli, Jun 12 2015]
MATHEMATICA
Table[n^8 - 1, {n, 33}] (* or *) LinearRecurrence[{9, -36, 84, -126, 126, -84, 36, -9, 1}, {0, 255, 6560, 65535, 390624, 1679615, 5764800, 16777215, 43046720}, 40]
PROG
(Magma) [n^8-1: n in [1..40]];
CROSSREFS
Cf. similar sequences listed in A258807.
Sequence in context: A261032 A069093 A024006 * A321553 A321547 A221970
KEYWORD
nonn,easy
AUTHOR
Vincenzo Librandi, Jun 11 2015
STATUS
approved