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Expansion of g.f. (1-6*x+7*x^2)/(1-7*x+11*x^2-x^3).
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%I #26 Aug 18 2024 14:36:44

%S 1,1,3,11,45,197,895,4143,19353,90793,426811,2008307,9454021,44513581,

%T 209609143,987068631,4648293425,21889908177,103085198195,485455690843,

%U 2286142563933,10766070546453,50700381312751,238762035742207,1124396126301641,5295090872259961

%N Expansion of g.f. (1-6*x+7*x^2)/(1-7*x+11*x^2-x^3).

%H Vincenzo Librandi, <a href="/A216949/b216949.txt">Table of n, a(n) for n = 0..200</a>

%H Eric Marberg, <a href="http://arxiv.org/abs/1203.5738">Crossings and nestings in colored set partitions</a>, arXiv preprint arXiv:1203.5738 [math.CO], 2012-2013.

%H Lily Yen, <a href="https://doi.org/10.46298/dmtcs.2339">Arc-coloured permutations</a>, PSAC 2013, Paris, France, June 24-28, Proc. DMTCS (2013) 743-754.

%H Lily Yen, <a href="https://doi.org/10.37236/4080">Crossings and Nestings for Arc-Coloured Permutations and Automation</a>, Electronic Journal of Combinatorics, 22(1) (2015), #P1.14.

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (7,-11,1).

%t CoefficientList[Series[(1 - 6 x + 7 x^2)/(1 - 7 x + 11 x^2 - x^3), {x, 0, 30}], x] (* _Vincenzo Librandi_, Mar 11 2013 *)

%t LinearRecurrence[{7,-11,1},{1,1,3},30] (* _Harvey P. Dale_, Aug 18 2024 *)

%K nonn,easy

%O 0,3

%A _N. J. A. Sloane_, Sep 22 2012