A381269 a(n) = numerator( [x*y*z]^n 1/sqrt((1 - (x + y + z))*(1 - y - z^2)) ).

1, 9, 1695, 26215, 120986775, 9502702209, 789204625209, 34080236440965, 1551341154742525575, 141040042903795882275, 52208336916743049297255, 306352374268280009960745, 1862930539686953773794528225, 178800539000323387892726124675, 34618577499107880715911257143875

Offset

0,2

Links

Table of n, a(n) for n=0..14.

S. Hassani, J.-M. Maillard, and N. Zenine, On the diagonals of rational functions: the minimal number of variables (unabridged version), arXiv:2502.05543 [math-ph], 2025. See p. 28.

Mathematica

a[n_]:=Numerator[SeriesCoefficient[1/Sqrt[(1-(x+y+z))(1-y-z^2)], {x, 0, n}, {y, 0, n}, {z, 0, n}]]; Array[a, 15, 0]

Crossrefs

Cf. A381270 (denominator).

Cf. A381271, A381272.

Sequence in context: A197804 A047944 A322245 * A251700 A246115 A068182

Adjacent sequences: A381266 A381267 A381268 * A381270 A381271 A381272

Keyword

nonn,frac

Author

Stefano Spezia, Feb 18 2025

Status

approved