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A220433
Expansion of e.g.f. for operads for alia algebras.
2
0, 1, 2, 11, 100, 1270, 20720, 413000, 9726640, 264279400, 8137329200, 280012733000, 10649265827200, 443563134414400, 20081317352096000, 981847343837360000, 51561200079861472000, 2894410559695262608000, 172959683650895741600000, 10961750255473947129200000
OFFSET
0,3
COMMENTS
This sequence, A220434 and A220435 are based on the e.g.f. in Proposition 3.5.2. The paper contains 3 more e.g.f.'s in Examples 3.5.3, 3.5.6 and 3.5.11 which will produce 9 more sequences, in case someone would like to add them.
LINKS
Olivier Bodini, Matthieu Dien, Antoine Genitrini, and Alfredo Viola, Beyond series-parallel concurrent systems: the case of arch processes, arXiv:1803.00843 [cs.DM], 2018.
Murray Bremner and Vladimir Dotsenko, Associator dependent algebras and Koszul duality, Annali di Matematica Pura ed Applicata, Vol. 202, No. 3 (2023), pp. 1233-1254; arXiv preprint, arXiv:2203.11142 [math.RA], 2022.
Anton Khoroshkin and Dmitri Piontkovski, On generating series of finitely presented operads, Journal of Algebra, Vol. 426 (2015), pp. 377-429; arXiv preprint, arXiv:1202.5170 [math.QA], 2012-2014. See Prop. 3.5.2.
FORMULA
Conjecture: D-finite with recurrence 4*a(n) +6*(-2*n+3)*a(n-1) -(3*n-5)*(3*n-7)*a(n-2)=0. - R. J. Mathar, Feb 27 2023
E.g.f.: series reversion of t-t^2+1/6*t^3. - Paul Laubie, Nov 07 2023
MATHEMATICA
With[{m = 19}, CoefficientList[InverseSeries[Series[x^3/6 - x^2 + x, {x, 0, m}]], x] * Range[0, m]!] (* Amiram Eldar, May 03 2024 *)
PROG
(PARI) lista(m) = {A = z + O(z); for (n= 1, m, A = z + A^2 - A^3/6; ); for (n=0, m, print1(n!*polcoeff(A, n, z), ", ")); } \\ Michel Marcus, Feb 12 2013
(PARI) concat([0], Vec( serlaplace( serreverse( t-t^2+1/6*t^3+O(t^22) ) ) ) ) \\ Joerg Arndt, Nov 08 2023
CROSSREFS
Sequence in context: A099169 A143135 A205806 * A318007 A243950 A056732
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Dec 16 2012
EXTENSIONS
More terms from Michel Marcus, Feb 12 2013
STATUS
approved