A220433 Expansion of e.g.f. for operads for alia algebras.

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

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

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, arXiv:2203.11142 [math.RA], 2022.

Anton Khoroshkin and Dmitri Piontkovski, On generating series of finitely presented operads, 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

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

Cf. A220434, A220435.

Sequence in context: A099169 A143135 A205806 * A318007 A243950 A056732

Adjacent sequences: A220430 A220431 A220432 * A220434 A220435 A220436

Keyword

nonn

Author

N. J. A. Sloane, Dec 16 2012

Extensions

More terms from Michel Marcus, Feb 12 2013

Status

approved