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A254468 a(n) = 35*4^n + 126*2^n + 70*3^n + 15*5^n + 5*6^n + 7^n + 210. 2
462, 924, 2508, 8646, 35112, 159654, 787968, 4137966, 22807752, 130656534, 772253328, 4683193086, 29012227992, 182964472614, 1171328741088, 7594839621006, 49780643849832, 329318254755894, 2195866174387248, 14741498331453726, 99542297086537272 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

This is the sequence of seventh 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 (28,-322,1960,-6769,13132,-13068,5040).

FORMULA

G.f.: -6*(259610*x^6 -461263*x^5 +319473*x^4 -111595*x^3 +20900*x^2 -2002*x +77) / ((x -1)*(2*x -1)*(3*x -1)*(4*x -1)*(5*x -1)*(6*x -1)*(7*x -1)). - Colin Barker, Jan 31 2015

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). - Colin Barker, Jan 31 2015

MATHEMATICA

Table[35 4^n + 126 2^n + 70 3^n + 15 5^n + 5 6^n + 7^n + 210, {n, 0, 25}] (* Michael De Vlieger, Jan 31 2015 *)

LinearRecurrence[{28, -322, 1960, -6769, 13132, -13068, 5040}, {462, 924, 2508, 8646, 35112, 159654, 787968}, 30] (* Harvey P. Dale, Dec 29 2019 *)

PROG

(PARI) vector(30, n, n--; 35*4^n + 126*2^n + 70*3^n + 15*5^n + 5*6^n + 7^n + 210) \\ Colin Barker, Jan 31 2015

CROSSREFS

Cf. A168614, A254368, A254369, A254370, A254467.

Sequence in context: A108749 A267740 A334408 * A242321 A222342 A246476

Adjacent sequences:  A254465 A254466 A254467 * A254469 A254470 A254471

KEYWORD

nonn,easy

AUTHOR

Luciano Ancora, Jan 31 2015

STATUS

approved

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Last modified November 30 05:00 EST 2021. Contains 349418 sequences. (Running on oeis4.)