OFFSET
0,1
COMMENTS
This is the sequence of sixth terms of "fourth partial sums of m-th powers".
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 (21,-175,735,-1624,1764,-720).
FORMULA
G.f.: -6*(10036*x^5 -16454*x^4 +10065*x^3 -2905*x^2 +399*x -21) / ((x -1)*(2*x -1)*(3*x -1)*(4*x -1)*(5*x -1)*(6*x -1)). - Colin Barker, Jan 31 2015
a(n) = 21*a(n-1)-175*a(n-2)+735*a(n-3)-1624*a(n-4)+1764*a(n-5)-720*a(n-6). - Colin Barker, Jan 31 2015
MATHEMATICA
Table[35 2^n + 10 4^n + 20 3^n + 4 5^n + 6^n + 56, {n, 0, 24}] (* Michael De Vlieger, Jan 31 2015 *)
LinearRecurrence[{21, -175, 735, -1624, 1764, -720}, {126, 252, 672, 2232, 8592, 36552}, 30] (* Harvey P. Dale, Aug 02 2024 *)
PROG
(PARI) vector(30, n, n--; 35*2^n + 10*4^n + 20*3^n + 4*5^n + 6^n + 56) \\ Colin Barker, Jan 31 2015
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Luciano Ancora, Jan 31 2015
STATUS
approved