OFFSET
0,1
COMMENTS
a(m,n) is a polynomial in m of degree n.
For any integers m>=0, n>=0, 2 * Integral_{t=-m..m} T_n(t/2)*exp(-t)*dt = 4 * Integral_{z=-m/2..m/2} T_n(z)*exp(-2*z)*dz = A300481(m,n)*exp(m) - a(m,n)*exp(-m).
FORMULA
EXAMPLE
Array starts with:
m=0: 2, 1, 0, 3, 18, 95, 592, ...
m=1: 2, 2, 3, 10, 47, 256, 1610, ...
m=2: 2, 3, 8, 29, 130, 697, 4376, ...
m=3: 2, 4, 15, 66, 327, 1838, 11770, ...
m=4: 2, 5, 24, 127, 722, 4459, 30248, ...
...
PROG
(PARI) { A300480(m, n) = if(n==0, return(2)); subst( serlaplace( 2*polchebyshev(n, 1, (x+m)/2)), x, 1); }
CROSSREFS
Values for m<=0 are given in A300481.
KEYWORD
nonn,tabl
AUTHOR
Max Alekseyev, Mar 06 2018
STATUS
approved