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A102761 Same as A000179, except that a(0) = 2 and a(1) = -1. 11
2, -1, 0, 1, 2, 13, 80, 579, 4738, 43387, 439792, 4890741, 59216642, 775596313, 10927434464, 164806435783, 2649391469058, 45226435601207, 817056406224416, 15574618910994665, 312400218671253762, 6577618644576902053 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

Created to simplify the formula for A000186.

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..21.

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], (14-August-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

PROG

(PARI) { A102761(n) = if(n==0, return(2)); subst( serlaplace( 2*polchebyshev(n, 1, (x-2)/2)), x, 1); } \\ Max Alekseyev, Mar 06 2018

CROSSREFS

Row m=2 in A300481.

Cf. A000023, A000179, A000186, A300484.

Sequence in context: A089631 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

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Last modified November 14 14:50 EST 2018. Contains 317208 sequences. (Running on oeis4.)