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A081683
a(n) = (10^n - 9^n - 8^n - 7^n + 4*6^n)/2.
1
1, 5, 25, 140, 1063, 11240, 137695, 1708040, 20564863, 239159480, 2699431615, 29751433640, 321858414463, 3431866061720, 36180197308735, 378028837122440, 3921778171748863, 40453047305219960, 415334396211141055, 4248035819012910440, 43312122701899432063, 440443420385055546200
OFFSET
0,2
COMMENTS
Binomial transform of A081681.
FORMULA
G.f.: -(5862*x^4 - 2685*x^3 + 460*x^2 - 35*x + 1)/((6*x-1)*(7*x-1)*(8*x-1)*(9*x-1)*(10*x-1)). - Colin Barker, Sep 07 2012
From Elmo R. Oliveira, Sep 15 2024: (Start)
E.g.f.: exp(6*x)*(exp(x)*(exp(3*x) - exp(2*x) - exp(x) - 1) + 4)/2.
a(n) = 40*a(n-1) - 635*a(n-2) + 5000*a(n-3) - 19524*a(n-4) + 30240*a(n-5) for n > 4. (End)
MATHEMATICA
Table[(10^n-9^n-8^n-7^n+4*6^n)/2, {n, 0, 20}] (* or *) LinearRecurrence[{40, -635, 5000, -19524, 30240}, {1, 5, 25, 140, 1063}, 20] (* Harvey P. Dale, Mar 27 2019 *)
CROSSREFS
Cf. A081681.
Sequence in context: A365772 A094094 A344249 * A064311 A122441 A114870
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Mar 30 2003
EXTENSIONS
a(19)-a(21) from Elmo R. Oliveira, Sep 15 2024
STATUS
approved