|
%I #39 Nov 08 2021 02:02:53
%S 1,2,15,204,3905,96030,2883167,102213944,4178507265,193501094490,
%T 10011386405999,572335117886532,35827847605137601,2437406399741075126,
%U 179059769134174484415,14127079203550978667760,1191321539697176278429697,106935795565608726499866930
%N a(n) = U_{n}(n) where U_{n}(x) is a Chebyshev polynomial of the second kind.
%H Seiichi Manyama, <a href="/A323118/b323118.txt">Table of n, a(n) for n = 0..351</a>
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Chebyshev_polynomials">Chebyshev polynomials</a>.
%F a(n) = Sum_{k=0..floor(n/2)} (n^2-1)^k*n^(n-2*k) * binomial(n+1,2*k+1).
%F a(n) ~ 2^n * n^n. - _Vaclav Kotesovec_, Jan 05 2019
%F a(n) = Sum_{k=0..n} (2*n-2)^(n-k) * binomial(2*n+1-k,k) = Sum_{k=0..n} (2*n-2)^k * binomial(n+1+k,2*k+1). - _Seiichi Manyama_, Mar 03 2021
%t Table[ChebyshevU[n, n], {n, 0, 20}] (* _Vaclav Kotesovec_, Jan 05 2019 *)
%o (PARI) a(n) = polchebyshev(n, 2, n);
%o (PARI) a(n) = sum(k=0, n\2, (n^2-1)^k*n^(n-2*k)*binomial(n+1, 2*k+1));
%o (PARI) a(n) = sum(k=0, n, (2*n-2)^k*binomial(n+1+k, 2*k+1)); \\ _Seiichi Manyama_, Mar 03 2021
%Y Main diagonal of A323182.
%Y Cf. A115066, A318192, A323117, A349073, A349074, A349075, A349076.
%K nonn
%O 0,2
%A _Seiichi Manyama_, Jan 05 2019
|
