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%I #24 Nov 01 2019 02:57:39
%S 1,1,2,6,21,82,354,1671,8536,46814,273907,1700828,11158746,77057021,
%T 558234902,4230337018,33448622893,275322101318,2354401779494,
%U 20878592918183,191682453823420,1819147694792802,17822073621801123
%N Essentially shifts 1 place right under inverse binomial transform.
%C With leading 0 and offset 1, number of permutations beginning with 21 and avoiding 3-12. - _Ralf Stephan_, Apr 25 2004
%H N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>
%H Sergey Kitaev, <a href="https://www.emis.de/journals/SLC/wpapers/s48kitaev.html">Generalized pattern avoidance with additional restrictions</a>, Sem. Lothar. Combinat. 48 (2003), Article B48e.
%H Sergey Kitaev, <a href="http://dx.doi.org/10.1016/j.disc.2004.03.017">Partially Ordered Generalized Patterns</a>, Discrete Math. 298(1-3) (2005), 212-229.
%H Sergey Kitaev and Toufik Mansour, <a href="https://arxiv.org/abs/math/0205182">Simultaneous avoidance of generalized patterns</a>, arXiv:math/0205182 [math.CO], 2002.
%F With offset 1, e.g.f.: x + exp(exp(x)) * int[0..x, exp(-exp(t))*sum(n>=1, t^n/n!) dt]. - _Ralf Stephan_, Apr 25 2004
%t max = 23; f[x_] = x + Exp[Exp[x]]*Integrate[Exp[-Exp[t]]*Sum[t^n/n!, {n, 1, max}], {t, 0, x}]; Rest[ CoefficientList[ Series[f[x], {x, 0, max}], x]*Range[0, max]!] (* _Jean-François Alcover_, Aug 07 2012, after _Ralf Stephan_ *)
%Y Cf. A032347, A046934.
%K nonn,nice,easy,eigen
%O 0,3
%A Joe K. Crump (joecr(AT)carolina.rr.com)
%E Last digit of a(22) corrected by _Jean-François Alcover_, Aug 07 2012
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