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%I #19 Jun 05 2019 12:09:54
%S 1,1,3,13,99,1021,12723,185053,3076419,57537661,1195682643,
%T 27332056093,681580659939,18412990131901,535693115608563,
%U 16698252859863133,555206734009942659,19614053492975935741,733674744650794446483,28968157934685913430173
%N Labeled graded semiorders.
%H Yan X Zhang, <a href="http://arxiv.org/abs/1508.00318">Four Variations on Graded Posets</a>, arXiv preprint arXiv:1508.00318 [math.CO], 2015. See Fig. 6.
%F Zhang (2015) gives e.g.f.
%p S := 1+x+x^2/(1-x-x^2) ;
%p Ex := subs(x=e^x-1,S) ;
%p taylor(%,x=0,23) ;
%p subs(log(e)=1,%) ;
%p L := gfun[seriestolist](%) ;
%p for i from 1 to nops(L) do
%p printf("%d,",op(i,L)*(i-1)!) ;
%p end do: # _R. J. Mathar_, May 11 2016
%t terms = 20;
%t egf = (1 + x + x^2/(1 - x - x^2) /. x -> E^x - 1) + O[x]^terms;
%t CoefficientList[egf, x]*Range[0, terms-1]! (* _Jean-François Alcover_, Sep 14 2018 *)
%t Table[1 + Sum[k!*Fibonacci[k-1]*StirlingS2[n, k], {k, 1, n}], {n, 0, 20}] (* _Vaclav Kotesovec_, Jun 05 2019 *)
%o (PARI) default(seriesprecision, 30); f = subst(1 + x + x^2/(1 - x - x^2), x, exp(x)-1); Vec(serlaplace(f)) \\ _Michel Marcus_, Sep 14 2018
%K nonn
%O 0,3
%A _N. J. A. Sloane_, Jan 28 2016
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