A102761 Same as A000179, except that a(0) = 2.

2, -1, 0, 1, 2, 13, 80, 579, 4738, 43387, 439792, 4890741, 59216642, 775596313, 10927434464, 164806435783, 2649391469058, 45226435601207, 817056406224416, 15574618910994665, 312400218671253762, 6577618644576902053, 145051250421230224304, 3343382818203784146955, 80399425364623070680706, 2013619745874493923699123

Offset: 0

Author

N. J. A. Sloane, Apr 04 2010, following a suggestion from Vladimir Shevelev

Keywords

• sign
• easy

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 = a(n)*exp(2) - A300484(n)*exp(-2). - Max Alekseyev, Mar 08 2018

References

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

Links

• Vladimir Shevelev, Spectrum of permanent's values and its extremal magnitudes in Λ_n^3 and Λ_n(α,β,γ), arXiv:1104.4051 [math.CO], 2011.

Crossrefs

Row m=2 in A300481.

Cf. A000023, A000179, A000186, A300484.

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

Programs

PARI

{ A102761(n) = subst( serlaplace( 2*polchebyshev(n, 1, (x-2)/2)), x, 1); } \\ Max Alekseyev, Mar 06 2018

Formula

a(n) = Sum_{i=0..n} A127672(n,i) * A000023(i). - Max Alekseyev, Mar 06 2018

a(n) = A300481(2,n) = A300480(-2,n). - Max Alekseyev, Mar 06 2018

a(n) = A335391(0,n) (Touchard). - William P. Orrick, Aug 29 2020

Extensions

Changed a(0)=2 (making the sequence more consistent with existing formulae) by Max Alekseyev, Mar 06 2018