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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

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: A125207 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

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Last modified July 26 02:06 EDT 2021. Contains 346294 sequences. (Running on oeis4.)