The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 56th year, we are closing in on 350,000 sequences, and we’ve crossed 9,700 citations (which often say “discovered thanks to the OEIS”).

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A189244 The n-th derivative of e^((2-x-x^2)/(1-x-x^2)), evaluated at x=1. 1
 1, 3, -7, 9, 177, -3897, 65649, -1057851, 16606977, -238404789, 2305262889, 33442089057, -3560906733903, 182521828278351, -8055082800686367, 338022326927690397, -13915405899740874879, 566988435851123595411, -22784764731442383689127, 888283409438427072329529 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS The n-th derivative of exp((2-x-x^2)/(1-x-x^2) is A(n,x) = n!*sum(m=1..n, sum(k=m..n, binomial(k-1,m-1)*binomial(k,n-k)*(2*x+1)^(2*k-n) * (-x^2-x+1)^(-m-k))/m!). LINKS Alois P. Heinz, Table of n, a(n) for n = 0..388 Vladimir Kruchinin, Derivation of Bell Polynomials of the Second Kind, arXiv:1104.5065 [math.CO], 2011. FORMULA a(n) = n!*sum(m=1..n, sum(k=m..n, binomial(k-1,m-1) *binomial(k,n-k) * (-1)^(m+k)*3^(2*k-n))/m!), a(0)=1. E.g.f.: exp(x*(3+x)/(3*x+x^2+1)). - Alois P. Heinz, Sep 27 2016 MATHEMATICA f[x_] := E^((2 - x - x^2)/(1 - x - x^2)); a[n_] := Derivative[n][f][1]; Table[a[n], {n, 0, 20}] (* Jean-François Alcover, Jul 27 2018 *) PROG (Maxima) a(n):=n!*sum(sum(binomial(k-1, m-1)*binomial(k, n-k)*(-1)^(m+k) * 3^(2*k-n), k, m, n)/m!, m, 1, n) CROSSREFS Sequence in context: A337613 A152607 A118559 * A127789 A112105 A065501 Adjacent sequences:  A189241 A189242 A189243 * A189245 A189246 A189247 KEYWORD sign AUTHOR Vladimir Kruchinin, Apr 26 2011 STATUS approved

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

Last modified December 5 14:32 EST 2021. Contains 349557 sequences. (Running on oeis4.)