A102761 - OEIS

%I #33 Aug 29 2020 13:13:59

%S 2,-1,0,1,2,13,80,579,4738,43387,439792,4890741,59216642,775596313,

%T 10927434464,164806435783,2649391469058,45226435601207,

%U 817056406224416,15574618910994665,312400218671253762,6577618644576902053,145051250421230224304,3343382818203784146955,80399425364623070680706,2013619745874493923699123

%N Same as A000179, except that a(0) = 2.

%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 = a(n)*exp(2) - A300484(n)*exp(-2). - _Max Alekseyev_, Mar 08 2018

%D J. Riordan, An Introduction to Combinatorial Analysis, Wiley, 1958, p. 197.

%H Vladimir Shevelev, <a href="http://arxiv.org/abs/1104.4051">Spectrum of permanent's values and its extremal magnitudes in Λ_n^3 and Λ_n(α,β,γ)</a>, arXiv:1104.4051 [math.CO], 2011.

%F a(n) = Sum_{i=0..n} A127672(n,i) * A000023(i). - _Max Alekseyev_, Mar 06 2018

%F a(n) = A300481(2,n) = A300480(-2,n). - _Max Alekseyev_, Mar 06 2018

%F a(n) = A335391(0,n) (Touchard). - _William P. Orrick_, Aug 29 2020

%o (PARI) { A102761(n) = subst( serlaplace( 2*polchebyshev(n, 1, (x-2)/2)), x, 1); } \\ _Max Alekseyev_, Mar 06 2018

%Y Row m=2 in A300481.

%Y Cf. A000023, A000179, A000186, A300484.

%Y A000179, A102761, and A335700 are all essentially the same sequence but with different conventions for the initial terms a(0) and a(1). - _N. J. A. Sloane_, Aug 06 2020

%K sign,easy

%O 0,1

%A _N. J. A. Sloane_, Apr 04 2010, following a suggestion from _Vladimir Shevelev_

%E Changed a(0)=2 (making the sequence more consistent with existing formulae) by _Max Alekseyev_, Mar 06 2018