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%I #24 Dec 01 2017 11:50:11
%S 1,2,6,20,64,194,562,1570,4258,11266,29186,74242,185858,458754,
%T 1118210,2695170,6430722,15204354,35651586,82968578,191758338,
%U 440401922,1005584386,2283798530,5161091074,11609833474,26004684802,58015612930,128949682178
%N Number of permutations of [n+1] avoiding 2413, 3142, 1324, 4231.
%H Andrei Asinowski and Toufik Mansour, <a href="https://arxiv.org/abs/0803.3414">Separable d-Permutations and Guillotine Partitions</a>, arXiv:0803.3414 [math.CO], 2008.
%H Andrei Asinowski and Toufik Mansour, <a href="https://doi.org/10.1007/s00026-010-0043-8">Separable d-Permutations and Guillotine Partitions</a>, Annals of Combinatorics 14 (1) pp.17-43 Springer, 2010.
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (9,-32,56,-48,16).
%F Andrei Asinowski and Toufik Mansour give a g.f.
%F G.f. -(-7*x+20*x^2-26*x^3+12*x^4+2*x^5+1)/((x-1)*(2*x-1)^4). - _R. J. Mathar_, Jan 04 2013
%F a(n) = 2+(n-1)*(n^2+n+42)*2^(n-4)/3 for n>0. - _R. J. Mathar_, Jan 30 2013 (see Maple section).
%p A220874 := proc(n)
%p if n = 0 then
%p 1;
%p else
%p 2+(n-1)*(n^2+n+42)*2^(n-4)/3 ;
%p end if;
%p end proc: # _R. J. Mathar_, Jan 30 2013
%t a[0] = 1; a[n_] := 2 + (n - 1)*(n^2 + n + 42)*2^(n - 4)/3;
%t Table[a[n], {n, 0, 28}] (* _Jean-François Alcover_, Dec 01 2017, after _R. J. Mathar_ *)
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_, Dec 27 2012