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%I #14 Oct 13 2015 03:07:26
%S 1,1,1,2,4,10,27,80,255,870,3155,12100,48871,207162,918944,4254690,
%T 20513838,102784942,534205629,2875098840,15999114433,91923562922,
%U 544606671776,3323112062994,20860869818386,134585869671342
%N Number of 2-sparse nonoverlapping partitions of n.
%H V. E. Adler, <a href="http://arxiv.org/abs/1510.02900">Set partitions and integrable hierarchies</a>, arXiv:1510.02900 [nlin.SI], 2015.
%H M. Klazar, <a href="http://kam.mff.cuni.cz/~klazar/bell.pdf">Bell numbers, their relatives and algebraic differential equations</a>
%H M. Klazar, <a href="http://dx.doi.org/10.1016/S0097-3165(03)00014-1">Bell numbers, their relatives and algebraic differential equations</a>, J. Combin. Theory, A 102 (2003), 63-87.
%o (PARI) {a(n)=local(A); if(n<0, 0, A=O(x^0); for(i=0,n\2, A=(1+x)/(1-x^2*subst(A,x,x/(1-x)))); polcoeff(A,n))} /* _Michael Somos_, Sep 22 2005 */
%K nonn,easy
%O 0,4
%A _N. J. A. Sloane_, Nov 12 2004