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A300485 a(n) = 2 * Integral_{t>=0} T_n((t-1)/2) * exp(-t) * dt, n>=0, where T_n(x) is n-th Chebyshev polynomial of first kind. 6
2, 0, -1, 2, 7, 34, 218, 1574, 12879, 117938, 1195479, 13294412, 160967522, 2108289364, 29703846535, 447990339602, 7201792686815, 122938198060734, 2220989581865882, 42336203570931402, 849191837620701239, 17879821236086808098 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

For any integer n>=0, 2 * Integral_{t=-1..1} T_n(t/2)*exp(-t)*dt = 4 * Integral_{z=-1/2..1/2} T_n(z)*exp(-2*z)*dz = a(n)*exp(1) - A300483(n)*exp(-1).

LINKS

Table of n, a(n) for n=0..21.

FORMULA

a(n) = Sum_{i=0..n} A127672(n,i) * A000166(i).

a(n) = A300481(1,n) = A300480(-1,n).

PROG

(PARI) { A300485(n) = if(n==0, return(2)); subst( serlaplace( 2*polchebyshev(n, 1, (x-1)/2)), x, 1); }

CROSSREFS

Row m=1 in A300481.

Cf. A102761, A300482, A300483, A300484.

Sequence in context: A318144 A260663 A241857 * A014511 A210572 A085855

Adjacent sequences:  A300482 A300483 A300484 * A300486 A300487 A300488

KEYWORD

sign

AUTHOR

Max Alekseyev, Mar 06 2018

STATUS

approved

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Last modified January 21 16:22 EST 2020. Contains 331114 sequences. (Running on oeis4.)