login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A291974 a(n) = (3*n)! * [z^(3*n)] exp(-(exp(z)/3 + 2*exp(-z/2)*cos(z*sqrt(3)/2)/3 - 1)). 4

%I

%S 1,-1,9,-197,6841,-254801,-3000807,3691567683,-717149457463,

%T -3166484321001,70729161470807849,-27375562310313650357,

%U -6307300288015827588199,14726712291264935798753279,-4956785715421801286491780487,-9984523503726123391084330853037

%N a(n) = (3*n)! * [z^(3*n)] exp(-(exp(z)/3 + 2*exp(-z/2)*cos(z*sqrt(3)/2)/3 - 1)).

%C Alternating row sums of A291451.

%H Alois P. Heinz, <a href="/A291974/b291974.txt">Table of n, a(n) for n = 0..205</a>

%p A291974 := proc(n) exp(-(exp(z)/3+2*exp(-z/2)*cos(z*sqrt(3)/2)/3-1)):

%p (3*n)!*coeff(series(%, z, 3*(n+1)), z, 3*n) end:

%p seq(A291974(n), n=0..15);

%p # second Maple program:

%p b:= proc(n, t) option remember; `if`(n=0, 1-2*t, add(

%p b(n-3*j, 1-t)*binomial(n-1, 3*j-1), j=1..n/3))

%p end:

%p a:= n-> b(3*n, 0):

%p seq(a(n), n=0..20); # _Alois P. Heinz_, Aug 14 2019

%Y Cf. A291451.

%K sign

%O 0,3

%A _Peter Luschny_, Sep 07 2017

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified September 28 06:00 EDT 2022. Contains 357063 sequences. (Running on oeis4.)