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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. 8

%I

%S 2,3,8,29,130,697,4376,31607,258690,2368847,24011832,267025409,

%T 3233119106,42346123861,596617706344,8998126507307,144651872924162,

%U 2469279716419035,44609768252582312,850345380011532261,17056474009400181122

%N 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.

%C 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).

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

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

%F 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).

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

%Y Row m=2 in A300480.

%Y Row sums of A156995.

%Y Cf. A102761, A300482, A300483, A300485.

%K nonn

%O 0,1

%A _Max Alekseyev_, Mar 06 2018

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Last modified January 26 14:08 EST 2020. Contains 331280 sequences. (Running on oeis4.)