A300485 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, 0, -1, 2, 7, 34, 218, 1574, 12879, 117938, 1195479, 13294412, 160967522, 2108289364, 29703846535, 447990339602, 7201792686815, 122938198060734, 2220989581865882, 42336203570931402, 849191837620701239, 17879821236086808098

Offset: 0

Author

Max Alekseyev, Mar 06 2018

Keywords

• sign

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 = a(n)*exp(1) - A300483(n)*exp(-1).

Crossrefs

Row m=1 in A300481.

Cf. A102761, A300482, A300483, A300484.

Programs

PARI

{ A300485(n) = if(n==0, return(2)); subst( serlaplace( 2*polchebyshev(n, 1, (x-1)/2)), x, 1); }

Formula

a(n) = Sum_{i=0..n} A127672(n,i) * A000166(i).

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