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Coefficients of inverse of Poincaré series [or Poincare series] of the 5-Gonal operad.
5

%I #23 Nov 11 2023 08:50:13

%S 1,5,38,347,3507,37788,425490,4947239,58944743,715930085,8831390152,

%T 110340491380,1393446215956,17758187064360,228091606247322,

%U 2949707761133535,38374765966463775,501891882459954495,6595106960772794310,87030030852121334835,1152846885317408648715

%N Coefficients of inverse of Poincaré series [or Poincare series] of the 5-Gonal operad.

%C Leroux asks: Is there a combinatorial interpretation for these numbers?

%C Those are the coefficients of the series reverse of the Poincaré series of the 5-Gonal operad, and not of the 5-Tetra operad. The sequence for the 5-Tetra operad is well-known and is A002294. - _Paul Laubie_, Nov 08 2023

%H Ph. Leroux, <a href="https://arxiv.org/abs/math/0512437">A simple symmetry generating operads related to rooted planar m-ary trees and polygonal numbers</a>, arXiv:math/0512437 [math.CO], 2005.

%H Ph. Leroux, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL10/Leroux/leroux1.html">A simple symmetry generating operads related to rooted planar m-ary trees and polygonal numbers</a>, J. Integer Seqs., 10 (2007), #07.4.7.

%F G.f.: series reversion of -(2*t^2-t)/(1+t)^3. - _Paul Laubie_, Nov 08 2023

%o (Sage) R.<t>=PowerSeriesRing(QQ); (-(2*t^2-t)/(1+t)^3).reverse().list()[1:] # _Paul Laubie_, Nov 08 2023

%K nonn

%O 1,2

%A _N. J. A. Sloane_, Jan 07 2006

%E New offset, name corrected and more terms from _Paul Laubie_, Nov 08 2023