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A267196 Labeled graded semiorders. 0
1, 1, 3, 13, 99, 1021, 12723, 185053, 3076419, 57537661, 1195682643, 27332056093, 681580659939, 18412990131901, 535693115608563, 16698252859863133, 555206734009942659, 19614053492975935741, 733674744650794446483, 28968157934685913430173 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
LINKS
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
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Jan 28 2016
STATUS
approved

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Last modified March 28 18:04 EDT 2024. Contains 371254 sequences. (Running on oeis4.)