OFFSET
1,2
LINKS
Muniru A Asiru, Table of n, a(n) for n = 1..5000
Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).
FORMULA
G.f.: x^2*(31 + 56*x + 36*x^2 - 4*x^3 + x^4)/(1 - x)^6.
a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6).
a(n) = -A024003(n). - Bruno Berselli, Jun 11 2015
Sum_{n>=2} 1/a(n) = Sum_{n>=1} (zeta(5*n) - 1) = 0.0379539032... - Amiram Eldar, Nov 06 2020
MAPLE
seq(n^5-1, n=1..35); # Muniru A Asiru, Oct 28 2018
MATHEMATICA
Table[n^5 - 1, {n, 1, 50}] (* or *) LinearRecurrence[{6, -15, 20, -15, 6, -1}, {0, 31, 242, 1023, 3124, 7775}, 50]
PROG
(Magma) [n^5-1: n in [1..50]];
(Magma) I:=[0, 31, 242, 1023, 3124, 7775]; [n le 6 select I[n] else 6*Self(n-1)-15*Self(n-2)+20*Self(n-3)-15*Self(n-4)+ 6*Self(n-5)-Self(n-6): n in [1..50]];
(SageMath) [n^5-1 for n in (1..50)] # Bruno Berselli, Jun 11 2015
(PARI) a(n)=n^5-1 \\ Charles R Greathouse IV, Jun 11 2015
(GAP) List([1..35], n->n^5-1); # Muniru A Asiru, Oct 28 2018
(Python) for n in range(1, 50): print(n**5 - 1, end=', ') # Stefano Spezia, Oct 28 2018
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Vincenzo Librandi, Jun 11 2015
STATUS
approved
