A342168 a(n) = U(n, (n+3)/2) where U(n, x) is a Chebyshev polynomial of the 2nd kind.

1, 4, 24, 204, 2255, 30744, 499121, 9409960, 202176360, 4878316860, 130651068911, 3846719565780, 123517560398401, 4296240885694576, 160935647131239840, 6460088606857290384, 276655979838719058119, 12591439417867717440180, 606947064800948702246681

Offset

0,2

Links

Seiichi Manyama, Table of n, a(n) for n = 0..386

Wikipedia, Chebyshev polynomials.

Formula

a(n) = Sum_{k=0..n} (n+1)^(n-k) * binomial(2*n+1-k,k) = Sum_{k=0..n} (n+1)^k * binomial(n+1+k,2*k+1).

a(n) ~ exp(3) * n^n. - Vaclav Kotesovec, May 06 2021

Mathematica

Table[ChebyshevU[n, (n + 3)/2], {n, 0, 18}] (* Amiram Eldar, Apr 27 2021 *)

Prog

(PARI) a(n) = polchebyshev(n, 2, (n+3)/2);
(PARI) a(n) = sum(k=0, n, (n+1)^(n-k)*binomial(2*n+1-k, k));
(PARI) a(n) = sum(k=0, n, (n+1)^k*binomial(n+1+k, 2*k+1));

Crossrefs

Cf. A097690, A097691, A323118, A342167.

Sequence in context: A089946 A343094 A012244 * A240429 A240297 A050388

Adjacent sequences: A342165 A342166 A342167 * A342169 A342170 A342171

Keyword

nonn

Author

Seiichi Manyama, Mar 03 2021

Status

approved