OFFSET
1,2
LINKS
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
KEYWORD
nonn
AUTHOR
Michel Marcus, Feb 21 2019
STATUS
approved