A254464 a(n) = 21*2^n + 10*4^n + 15*3^n + 3*6^n + 6*5^n + 7^n + 28.
84, 210, 714, 2982, 14178, 73470, 404634, 2331462, 13906578, 85232910, 533860554, 3403329942, 22012307778, 144090486750, 952693102074, 6352175272422, 42655384385778, 288161867586990, 1956674663089194, 13344181547374902, 91343993647708578, 627261876368085630
Offset: 0
Links
- Colin Barker, Table of n, a(n) for n = 0..1000
- Luciano Ancora, Demonstration of formulas, page 2.
- Luciano Ancora, Recurrence relations for partial sums of m-th powers.
- Index entries for linear recurrences with constant coefficients, signature (28,-322,1960,-6769,13132,-13068,5040).
Programs
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Mathematica
Table[21 2^n + 10 4^n + 15 3^n + 3 6^n + 6 5^n + 7^n + 28, {n, 0, 24}] (* Michael De Vlieger, Jan 31 2015 *) LinearRecurrence[{28,-322,1960,-6769,13132,-13068,5040},{84,210,714,2982,14178,73470,404634},30] (* Harvey P. Dale, May 17 2019 *) -
PARI
vector(30, n, n--; 21*2^n + 10*4^n + 15*3^n + 3*6^n + 6*5^n + 7^n + 28) \\ Colin Barker, Jan 31 2015
Formula
From Colin Barker, Jan 31 2015: (Start)
G.f.: -6*(40188*x^6 - 74058*x^5 + 52931*x^4 - 19005*x^3 + 3647*x^2 - 357*x + 14)/((x-1)*(2*x-1)*(3*x-1)*(4*x-1)*(5*x-1)*(6*x-1)*(7*x-1)).
a(n) = 28*a(n-1) - 322*a(n-2) + 1960*a(n-3) - 6769*a(n-4) + 13132*a(n-5) - 13068*a(n-6) + 5040*a(n-7). (End)
E.g.f.: exp(x)*(exp(x)*(exp(5*x) + 3*exp(4*x) + 6*exp(3*x) + 10*exp(2*x) + 15*exp(x) + 21) + 28). - Elmo R. Oliveira, Sep 16 2024
Comments