A324312 Expansion of the generating function of rooted planar Eulerian orientations, counted by edges.

1, 5, 33, 252, 2108, 18774, 175045, 1690260, 16779012, 170335360, 1761496828, 18501861600, 196928222832, 2120156504636, 23054547056085, 252901313956980, 2795875813360980, 31123866089539440, 348634514260163164, 3927223348115402400, 44464453793202573936, 505773761881655080800

Offset

1,2

Links

Table of n, a(n) for n=1..22.

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 1.

Formula

G.f.: (1/(4t^2))*(t-2t^2-R(t)) where R(t) is A324311.

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)^2/(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 - 2*t^2 - R)/(4*t^2), k, t)); }

Crossrefs

Cf. A324311, A324313, A324314.

Sequence in context: A367280 A171804 A365182 * A225612 A330802 A199552

Adjacent sequences: A324309 A324310 A324311 * A324313 A324314 A324315

Keyword

nonn

Author

Michel Marcus, Feb 21 2019

Status

approved