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
KEYWORD
nonn,easy
AUTHOR
Luciano Ancora, Jan 27 2015
STATUS
approved