A300483 a(n) = 2 * Integral_{t>=0} T_n((t+1)/2) * exp(-t) * dt, n>=0, where T_n(x) is n-th Chebyshev polynomial of first kind.

2, 2, 3, 10, 47, 256, 1610, 11628, 95167, 871450, 8833459, 98233158, 1189398050, 15578268382, 219483388403, 3310225751098, 53214450175743, 908397242172212, 16411016615547530, 312824583201360248, 6274726126933368879, 132115002152296986730, 2913432246090160413827

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) = Sum_{i=0..n} A127672(n,i) * A000522(i).

a(n) = A300480(1,n) = A300481(-1,n).

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

Row m=1 in A300480.

Cf. A102761, A300482, A300484, A300485.

Sequence in context: A220644 A338372 A153920 * A294241 A067579 A019143

Adjacent sequences: A300480 A300481 A300482 * A300484 A300485 A300486

Keyword

nonn

Author

Max Alekseyev, Mar 06 2018

Status

approved