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A254370
a(n) = 35*2^n + 5*4^n + 15*3^n + 5^n + 70.
5
126, 210, 450, 1200, 3750, 13080, 49350, 197400, 825750, 3577080, 15930150, 72528600, 336141750, 1580449080, 7518010950, 36102667800, 174710721750, 850780489080, 4164115131750, 20465328135000, 100917328245750, 498984369457080, 2472617583932550
OFFSET
0,1
COMMENTS
This is the sequence of fifth terms of "fifth partial sums of m-th powers".
FORMULA
G.f.: -6*(1879*x^4-2675*x^3+1335*x^2-280*x+21) / ((x-1)*(2*x-1)*(3*x-1)*(4*x-1)*(5*x-1)). - Colin Barker, Jan 30 2015
a(n) = 15*a(n-1)-85*a(n-2)+225*a(n-3)-274*a(n-4)+120*a(n-5). - Colin Barker, Jan 30 2015
MATHEMATICA
Table[35 2^n + 5 4^n + 15 3^n + 5^n + 70, {n, 0, 30}] (* Bruno Berselli, Jan 30 2015 *)
PROG
(PARI) vector(30, n, n--; 35*2^n + 5*4^n + 15*3^n + 5^n + 70) \\ Colin Barker, Jan 30 2015
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Luciano Ancora, Jan 30 2015
STATUS
approved