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A003123
Number of Hamiltonian rooted triangulations with n internal nodes and 4 external nodes.
(Formerly M2038)
2
2, 12, 92, 800, 7554, 75664, 792448, 8595120, 95895816, 1095130728, 12753454896, 151017596448, 1814135701956, 22067487234504, 271407264938656, 3370796862212944, 42230992336570032, 533252038221313888, 6781213722509638192, 86790636905453265216
OFFSET
0,1
REFERENCES
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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
Sequence in context: A333473 A103882 A304979 * A316143 A372202 A359692
KEYWORD
nonn
EXTENSIONS
More terms and title clarified by Sean A. Irvine, Feb 02 2015
STATUS
approved