login
A323181
a(n) = U_{2*n-1}(n)/(2*n) where U_{n}(x) is a Chebyshev polynomial of the second kind.
1
1, 14, 1155, 238204, 92208005, 57723886506, 53303126198791, 68201766898127864, 115562692712642803209, 250568062566458497345990, 676789415690723540731574411, 2228525638897473760683321942900, 8788368165086865758098175776802701, 40895852668226096118083495224349942114
OFFSET
1,2
LINKS
FORMULA
a(n) = U_{n-1}(2*n^2-1).
a(n) = (1/2) * Sum_{k=0..n-1} binomial(2*n,2*k+1)*(n^2-1)^(n-1-k)*n^(2*k).
a(n) ~ 2^(2*n - 2) * n^(2*n - 2). - Vaclav Kotesovec, Jan 07 2019
MATHEMATICA
Table[ChebyshevU[2*n - 1, n]/(2*n), {n, 1, 15}] (* Vaclav Kotesovec, Jan 07 2019 *)
PROG
(PARI) {a(n) = polchebyshev(2*n-1, 2, n)/(2*n)}
(PARI) {a(n) = polchebyshev(n-1, 2, 2*n^2-1)}
(PARI) {a(n) = sum(k=0, n-1, binomial(2*n, 2*k+1)*(n^2-1)^(n-1-k)*n^(2*k))/2}
CROSSREFS
Sequence in context: A132504 A178989 A232373 * A206613 A198712 A204972
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Jan 06 2019
STATUS
approved