A267196 Labeled graded semiorders.

1, 1, 3, 13, 99, 1021, 12723, 185053, 3076419, 57537661, 1195682643, 27332056093, 681580659939, 18412990131901, 535693115608563, 16698252859863133, 555206734009942659, 19614053492975935741, 733674744650794446483, 28968157934685913430173

Offset

0,3

Links

Table of n, a(n) for n=0..19.

Yan X Zhang, Four Variations on Graded Posets, arXiv preprint arXiv:1508.00318 [math.CO], 2015. See Fig. 6.

Formula

Zhang (2015) gives e.g.f.

Maple

S := 1+x+x^2/(1-x-x^2) ;
Ex := subs(x=e^x-1, S) ;
taylor(%, x=0, 23) ;
subs(log(e)=1, %) ;
L := gfun[seriestolist](%) ;
for i from 1 to nops(L) do
    printf("%d, ", op(i, L)*(i-1)!) ;
end do: # R. J. Mathar, May 11 2016

Mathematica

terms = 20;
egf = (1 + x + x^2/(1 - x - x^2) /. x -> E^x - 1) + O[x]^terms;
CoefficientList[egf, x]*Range[0, terms-1]! (* Jean-François Alcover, Sep 14 2018 *)
Table[1 + Sum[k!*Fibonacci[k-1]*StirlingS2[n, k], {k, 1, n}], {n, 0, 20}] (* Vaclav Kotesovec, Jun 05 2019 *)

Prog

(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

Crossrefs

Sequence in context: A352300 A306082 A220897 * A268215 A323687 A338697

Adjacent sequences: A267193 A267194 A267195 * A267197 A267198 A267199

Keyword

nonn

Author

N. J. A. Sloane, Jan 28 2016

Status

approved