OFFSET
0,1
COMMENTS
For any integer n>=0, 2 * Integral_{t=-1..1} T_n(t/2)*exp(-t)*dt = 4 * Integral_{z=-1/2..1/2} T_n(z)*exp(-2*z)*dz = A300485(n)*exp(1) - a(n)*exp(-1).
LINKS
Robert Israel, Table of n, a(n) for n = 0..449
FORMULA
a(n) ~ exp(1) * n!. - Vaclav Kotesovec, Apr 15 2020
MAPLE
seq(2*int(orthopoly[T](n, (t+1)/2)*exp(-t), t=0..infinity), n=0..50); # Robert Israel, Mar 06 2018
MATHEMATICA
a[n_] := 2 Integrate[ChebyshevT[n, (t + 1)/2] Exp[-t], {t, 0, Infinity}];
Table[a[n], {n, 0, 22}] (* Jean-François Alcover, Feb 28 2019 *)
PROG
(PARI) { A300483(n) = if(n==0, return(2)); subst( serlaplace( 2*polchebyshev(n, 1, (x+1)/2)), x, 1); }
CROSSREFS
KEYWORD
nonn
AUTHOR
Max Alekseyev, Mar 06 2018
STATUS
approved