OFFSET
1,2
COMMENTS
LINKS
Paolo Xausa, Table of n, a(n) for n = 1..350
FORMULA
a(n) = Sum_{k = 1..n} (2^k)*n^(k-2)*binomial(n+k, 2*k)/(n + k) (shows that a(n) is an integer).
a(n) = (cos(n*arccos(n+1)) - 1)/n^3.
a(n) = (A342205(n) - 1)/n^3.
a(n) = ( (n + 1 + sqrt(n*(n+2)))^n + (n + 1 - sqrt(n*(n+2)))^n - 2 )/(2*n^3).
MAPLE
seq( simplify( (ChebyshevT(n, n+1) - 1)/n^3 ), n = 1..20);
MATHEMATICA
Array[(ChebyshevT[#, #+1]-1)/#^3 &, 20] (* Paolo Xausa, Mar 14 2024 *)
PROG
(Python)
from sympy import chebyshevt
def A370259(n): return (chebyshevt(n, n+1)-1)//n**3 # Chai Wah Wu, Mar 13 2024
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Peter Bala, Mar 11 2024
STATUS
approved