login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

a(n) = 2 * Integral_{t>=0} T_n(t/2) * exp(-t) * dt, n>=0, where T_n(x) is n-th Chebyshev polynomial of first kind.
6

%I #7 Mar 07 2018 08:19:06

%S 2,1,0,3,18,95,592,4277,35010,320589,3249648,36137959,437555090,

%T 5730924667,80743426272,1217763999465,19576502192898,334180669811993,

%U 6037275621582880,115081732852805771,2308342741080096402

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

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

%o (PARI) { A300482(n) = if(n==0, return(2)); subst( serlaplace( 2*polchebyshev(n, 1, x/2)), x, 1); }

%Y Row m=0 in A300480 and A300481.

%Y Cf. A102761, A300483, A300484, A300485.

%K nonn

%O 0,1

%A _Max Alekseyev_, Mar 06 2018