A324314 Expansion of the generating function of quartic rooted planar Eulerian orientations, counted by vertices.

4, 35, 402, 5334, 77472, 1197459, 19371000, 324457562, 5585968752, 98334394470, 1763204413488, 32108212934100, 592453862089920, 11056844466818451, 208406532039094530, 3962553996669046002, 75926241110870890200, 1464873759398352892050, 28437685246012526646228, 555153133514289017625900

Offset

1,1

Links

Table of n, a(n) for n=1..20.

Mireille Bousquet-Mélou, Andrew Elvey Price, Andrew Price, The generating function of planar Eulerian orientations, arXiv:1803.08265 [math.CO], 2018.

Mireille Bousquet-Mélou, Andrew Elvey Price, Paul Zinn-Justin, Eulerian orientations and the six-vertex model on planar map, arXiv:1902.07369 [math.CO], 2019. See Theorem 2.

Formula

G.f.: (1/(3t^2))*(t-3t^2-R(t)) where R(t) is A324313.

Prog

(PARI) lista(nn) = {nn += 2; my(v = vector(nn), R, P, c, r, s); kill(y); for (n=1, nn, v[n] = y; R = sum(k=1, n, v[k]*t^k); P = sum(k=0, n, binomial(2*k, k)*binomial(3*k, k)/(k+1)*R^(k+1)); c = polcoef(P, n, t); r = polcoef(c, 0, y); s = polcoef(c, 1, y); if (n==1, v[n] = (1-r)/s, v[n] = -r/s); ); R = sum(k=1, #v, v[k]*t^k); vector(nn-2, k, polcoef((t - 3*t^2 - R)/(3*t^2), k, t)); }

Crossrefs

Cf. A324311, A324312, A324313.

Sequence in context: A104456 A277868 A305905 * A123224 A160887 A277386

Adjacent sequences: A324311 A324312 A324313 * A324315 A324316 A324317

Keyword

nonn

Author

Michel Marcus, Feb 21 2019

Status

approved