

A102761


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


11



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
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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 = 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

Table of n, a(n) for n=0..25.
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.


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


PROG

(PARI) { A102761(n) = subst( serlaplace( 2*polchebyshev(n, 1, (x2)/2)), x, 1); } \\ Max Alekseyev, Mar 06 2018


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
Sequence in context: A332032 A298878 A195982 * A231119 A129558 A267181
Adjacent sequences: A102758 A102759 A102760 * A102762 A102763 A102764


KEYWORD

sign,easy


AUTHOR

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


EXTENSIONS

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


STATUS

approved



