A254146 a(n) = 1*8^n + 2*7^n + 3*6^n + 4*5^n + 5*4^n + 6*3^n + 7*2^n + 8*1^n.

36, 120, 540, 2892, 17172, 109020, 725220, 4992492, 35277012, 254402940, 1864757700, 13850340492, 103996064052, 787943896860, 6015370201380, 46217575406892, 357036252710292, 2770979252910780, 21591510288112260, 168818732978719692, 1323861500735007732

Offset

0,1

Comments

This is the sequence of eighth terms of "second partial sums of m-th powers".

Links

Colin Barker, Table of n, a(n) for n = 0..1000

Luciano Ancora, Demonstration of formulas

Index entries for linear recurrences with constant coefficients, signature (36,-546,4536,-22449,67284,-118124,109584,-40320).

Formula

G.f.: -12*(55308*x^7 - 113262*x^6 + 92327*x^5 - 39312*x^4 + 9527*x^3 - 1323*x^2 + 98*x -3) / ((x-1)*(2*x-1)*(3*x-1)*(4*x-1)*(5*x-1)*(6*x-1)*(7*x-1)*(8*x-1)). - Colin Barker, Jan 28 2015

From Peter Bala, Jan 31 2016: (Start)

a(n) = (x + 1)*( Bernoulli(n + 1, x + 1) - Bernoulli(n + 1, 1) )/(n + 1) - ( Bernoulli(n + 2, x + 1) - Bernoulli(n + 2, 1) )/(n + 2) at x = 8.

a(n) = 1/7!*Sum_{k = 0..n} (-1)^(k+n)*(k + 9)!*Stirling2(n,k)/ ((k + 1)*(k + 2)). (End)

a(n) = 36*a(n-1)-546*a(n-2)+4536*a(n-3)-22449*a(n-4)+67284*a(n-5)-118124*a(n-6)+109584*a(n-7)-40320*a(n-8). - Wesley Ivan Hurt, May 24 2021

Maple

seq(add(i*(9 - i)^n, i = 1..8), n = 0..20); # Peter Bala, Jan 31 2017

Mathematica

Table[7 2^n + 5 4^n + 8^n + 6 3^n + 3 6^n + 4 5^n + 2 7^n + 8, {n, 0, 30}] (* Vincenzo Librandi, Jan 28 2015 *)
LinearRecurrence[{36, -546, 4536, -22449, 67284, -118124, 109584, -40320}, {36, 120, 540, 2892, 17172, 109020, 725220, 4992492}, 30] (* Harvey P. Dale, Mar 02 2022 *)

Prog

(PARI) vector(30, n, n--; 7*2^n + 5*4^n + 8^n + 6*3^n + 3*6^n + 4*5^n + 2*7^n + 8) \\ Colin Barker, Jan 28 2015
(Magma) [7*2^n+5*4^n+8^n+6*3^n+3*6^n+4*5^n+2*7^n+8: n in [0..30]]; // Vincenzo Librandi, Jan 28 2015

Crossrefs

Cf. A052548, A254028, A254030, A254031, A254144, A254145.

Sequence in context: A242356 A165966 A307939 * A173420 A271736 A280886

Adjacent sequences: A254143 A254144 A254145 * A254147 A254148 A254149

Keyword

nonn,easy

Author

Luciano Ancora, Jan 27 2015

Status

approved