

A300484


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


8



2, 3, 8, 29, 130, 697, 4376, 31607, 258690, 2368847, 24011832, 267025409, 3233119106, 42346123861, 596617706344, 8998126507307, 144651872924162, 2469279716419035, 44609768252582312, 850345380011532261, 17056474009400181122
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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*nm, m)*(nm)!/(2*nm).


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 A188498 A012886
Adjacent sequences: A300481 A300482 A300483 * A300485 A300486 A300487


KEYWORD

nonn


AUTHOR

Max Alekseyev, Mar 06 2018


STATUS

approved



