A254370 a(n) = 35*2^n + 5*4^n + 15*3^n + 5^n + 70.

126, 210, 450, 1200, 3750, 13080, 49350, 197400, 825750, 3577080, 15930150, 72528600, 336141750, 1580449080, 7518010950, 36102667800, 174710721750, 850780489080, 4164115131750, 20465328135000, 100917328245750, 498984369457080, 2472617583932550

Offset

0,1

Comments

This is the sequence of fifth 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 (15,-85,225,-274,120).

Formula

G.f.: -6*(1879*x^4-2675*x^3+1335*x^2-280*x+21) / ((x-1)*(2*x-1)*(3*x-1)*(4*x-1)*(5*x-1)). - Colin Barker, Jan 30 2015

a(n) = 15*a(n-1)-85*a(n-2)+225*a(n-3)-274*a(n-4)+120*a(n-5). - Colin Barker, Jan 30 2015

Mathematica

Table[35 2^n + 5 4^n + 15 3^n + 5^n + 70, {n, 0, 30}] (* Bruno Berselli, Jan 30 2015 *)

Prog

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

Crossrefs

Cf. A168614, A254368, A254369.

Sequence in context: A267331 A267739 A290203 * A325932 A109024 A249190

Adjacent sequences: A254367 A254368 A254369 * A254371 A254372 A254373

Keyword

nonn,easy

Author

Luciano Ancora, Jan 30 2015

Status

approved