A220434 Numerators of reduced coefficients in expansion of e.g.f. for operads for alia algebras.

0, 1, 1, 11, 25, 127, 259, 1475, 17369, 943855, 2906189, 18182645, 43219423, 276950009, 447795895, 8757736405, 229953974953, 1518654958327, 45374710282075, 302708963291075, 1014053268490955, 20460600033239575, 4315372228473665, 29217669542549345, 1190372934615418775

Offset

0,4

Links

Table of n, a(n) for n=0..24.

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

Numerators of the rational sequence whose g.f. is the series reversion of x^3/6 - x^2 + x. - Amiram Eldar, May 03 2024

Example

Fractions begin: 0, 1, 1, 11/6, 25/6, 127/12, 259/9, 1475/18, 17369/72, 943855/1296, 2906189/1296, 18182645/2592, ... .

Mathematica

Numerator[CoefficientList[InverseSeries[Series[x^3/6 - x^2 + x, {x, 0, 25}]], x]] (* Amiram Eldar, May 03 2024 *)

Crossrefs

Cf. A220433, A220435 (denominators).

Sequence in context: A039337 A043160 A043940 * A191720 A066956 A250611

Adjacent sequences: A220431 A220432 A220433 * A220435 A220436 A220437

Keyword

nonn,frac

Author

N. J. A. Sloane, Dec 16 2012

Extensions

a(0) and more terms added by Amiram Eldar, May 03 2024

Status

approved