login
A349070
a(n) = T(3*n, n), where T(n, x) is the Chebyshev polynomial of the first kind.
5
1, 1, 1351, 3880899, 28355806081, 429364731169925, 11731978174095849671, 525735133485219615486151, 36049049892983023583045990401, 3588952618789973294871796462342089, 497937643558017209960022199517744044999, 93156956377055671178035977181412016527566091
OFFSET
0,3
COMMENTS
In general, for k>=1, T(k*n, n) ~ 2^(k*n - 1) * n^(k*n).
LINKS
Eric Weisstein's World of Mathematics, Chebyshev Polynomial of the First Kind.
FORMULA
a(n) = cosh(3*n*arccosh(n)).
a(n) = ((n + sqrt(n^2-1))^(3*n) + (n - sqrt(n^2-1))^(3*n))/2.
a(n) ~ 2^(3*n-1) * n^(3*n).
MATHEMATICA
Table[ChebyshevT[3*n, n], {n, 0, 13}]
PROG
(PARI) a(n) = polchebyshev(3*n, 1, n); \\ Michel Marcus, Nov 07 2021
CROSSREFS
KEYWORD
nonn
AUTHOR
Vaclav Kotesovec, Nov 07 2021
STATUS
approved