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

0,1

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).

Links

Table of n, a(n) for n=0..20.

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).

Prog

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

Crossrefs

Row m=2 in A300480.

Row sums of A156995.

Cf. A102761, A300482, A300483, A300485.

Sequence in context: A006277 A186927 A177010 * A004106 A332030 A188498

Adjacent sequences: A300481 A300482 A300483 * A300485 A300486 A300487

Keyword

nonn

Author

Max Alekseyev, Mar 06 2018

Status

approved