A254467 a(n) = 15*4^n + 70*2^n + 35*3^n + 5^(n+1) + 6^n + 126.

252, 462, 1122, 3432, 12342, 49632, 216342, 1001952, 4863462, 24500352, 127161462, 676195872, 3668030982, 20227217472, 113076824982, 639383508192, 3649985092902, 21003583828992, 121677813214902, 708891056106912, 4149610383537222

Offset

0,1

Comments

This is the sequence of sixth terms of "fifth 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*(21310*x^5 -34383*x^4 +20750*x^3 -5920*x^2 +805*x -42) / ((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[15×4^n+70×2^n+35×3^n+5^(n+1)+6^n+126, {n, 0, 25}] (* Michael De Vlieger, Jan 31 2015 *)
LinearRecurrence[{21, -175, 735, -1624, 1764, -720}, {252, 462, 1122, 3432, 12342, 49632}, 30] (* Harvey P. Dale, Jul 16 2018 *)

Prog

(PARI) vector(30, n, n--; 15*4^n + 70*2^n + 35*3^n + 5^(n+1) + 6^n + 126) \\ Colin Barker, Jan 31 2015

Crossrefs

Cf. A168614, A254368, A254369, A254370, A254468.

Sequence in context: A032800 A024749 A024757 * A242570 A046379 A250794

Adjacent sequences: A254464 A254465 A254466 * A254468 A254469 A254470

Keyword

nonn,easy

Author

Luciano Ancora, Jan 31 2015

Status

approved