OFFSET
0,1
REFERENCES
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
P. N. Rathie, The enumeration of Hamiltonian polygons in rooted planar triangulations, Discrete Math., 6 (1973), 163-168.
FORMULA
a(n) = f(n, 4) where f(n, k) is defined in A003122. - Sean A. Irvine, Feb 02 2015
PROG
(C#) See A003122
(PARI)
P(n, k) = k*(2*n+2*k-4)!*(2*n+k-1)!/((n+k-1)!*(n+k-2)!*n!*(n+k)!);
F(K, N=23) = {
my(x='x + O('x^(K+1)), t='t + O('t^(N+1)),
r='t*Ser(vector(N, n, sqr(binomial(2*n, n)/(n+1))), 't),
p=x^3*Ser(apply(k->Ser(vector(N, n, P(n-1, k)), 't), [3..K])),
s=serreverse(t*(1+r)), f=subst(subst(p, 't, s), 'x, 'x*s/'t));
Vec(polcoeff(f, K));
};
F(4) \\ Gheorghe Coserea, Aug 18 2017
CROSSREFS
KEYWORD
nonn
AUTHOR
EXTENSIONS
More terms and title clarified by Sean A. Irvine, Feb 02 2015
STATUS
approved