A113207 Coefficients of inverse of Poincaré series [or Poincare series] of the 5-Gonal operad.

1, 5, 38, 347, 3507, 37788, 425490, 4947239, 58944743, 715930085, 8831390152, 110340491380, 1393446215956, 17758187064360, 228091606247322, 2949707761133535, 38374765966463775, 501891882459954495, 6595106960772794310, 87030030852121334835, 1152846885317408648715

Offset

1,2

Comments

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

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

Links

Table of n, a(n) for n=1..21.

Ph. Leroux, A simple symmetry generating operads related to rooted planar m-ary trees and polygonal numbers, arXiv:math/0512437 [math.CO], 2005.

Ph. Leroux, A simple symmetry generating operads related to rooted planar m-ary trees and polygonal numbers, J. Integer Seqs., 10 (2007), #07.4.7.

Formula

G.f.: series reversion of -(2*t^2-t)/(1+t)^3. - Paul Laubie, Nov 08 2023

Prog

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

Crossrefs

Sequence in context: A370476 A369480 A365839 * A158266 A355380 A213639

Adjacent sequences: A113204 A113205 A113206 * A113208 A113209 A113210

Keyword

nonn

Author

N. J. A. Sloane, Jan 07 2006

Extensions

New offset, name corrected and more terms from Paul Laubie, Nov 08 2023

Status

approved