A300484 a(n) = 2 * Integral_{t>=0} T_n(t/2+1) * exp(-t) * dt, n>=0, where T_n(x) is n-th Chebyshev polynomial of first kind.

2, 3, 8, 29, 130, 697, 4376, 31607, 258690, 2368847, 24011832, 267025409, 3233119106, 42346123861, 596617706344, 8998126507307, 144651872924162, 2469279716419035, 44609768252582312, 850345380011532261, 17056474009400181122

Offset: 0

Author

Max Alekseyev, Mar 06 2018

Keywords

• nonn

Comments

For any integer n>=0, 2 * Integral_{t=-2..2} T_n(t/2)*exp(-t)*dt = 4 * Integral_{z=-1..1} T_n(z)*exp(-2*z)*dz = A102761(n)*exp(2) - a(n)*exp(-2).

Crossrefs

Row m=2 in A300480.

Row sums of A156995.

Cf. A102761, A300482, A300483, A300485.

Programs

PARI

{ A300484(n) = if(n==0, return(2)); subst( serlaplace( 2*polchebyshev(n, 1, (x+2)/2)), x, 1); }

Formula

a(n) = Sum_{i=0..n} A127672(n,i) * A010842(i).

a(n) = A300480(2,n) = A300481(-2,n).

a(n) = Sum_{m=0..n} A156995(n,m) = 2*n*Sum_{m=0..n} binomial(2*n-m, m)*(n-m)!/(2*n-m).