OFFSET
1,4
LINKS
Gheorghe Coserea, Table of n, a(n) for n = 1..150
Sergey Fomin and Grigory Mikhalkin, Labeled floor diagrams for plane curves, arXiv:0906.3828 [math.AG], 2009-2010.
Rahul Pandharipande, A geometric construction of Getzler's relation, arXiv:alg-geom/9705016, 1997.
MATHEMATICA
(* b = A013587 *) b[n_] := b[n] = If[n==1, 1, Sum[b[k] b[n-k] k^2 (n-k) (3k-n) (3n-4)!/(3k-1)!/(3(n-k)-2)!, {k, 1, n-1}]];
a[n_] := a[n] = Module[{t1, t2}, t1 = Binomial[n, 3] b[n]; t2 = Sum[ Binomial[3n-1, 3k-1](3k^2-2k)(n-k) b[k] a[n-k], {k, n-1}]; t1/12 + t2/9];
Array[a, 14] (* Jean-François Alcover, Oct 08 2018, after Gheorghe Coserea *)
PROG
(PARI)
A013587_seq(N) = {
my(a = vector(N), t1, t2); a[1] = 1;
for (n=2, N, a[n] = sum(k=1, n-1,
t1 = binomial(3*n-4, 3*k-2)*(k*(n-k))^2;
t2 = binomial(3*n-4, 3*k-1)*k^3*(n-k);
(t1 - t2)*a[k]*a[n-k])); a;
};
A171109_seq(N) = {
my(a = vector(N), b=A013587_seq(N), t1, t2);
for (n=3, N, t1 = binomial(n, 3)*b[n];
t2 = sum(k=1, n-1, binomial(3*n-1, 3*k-1)*(3*k^2-2*k)*(n-k)*b[k]*a[n-k]);
a[n] = (t1/12 + t2/9)); a;
};
A171109_seq(14) \\ Gheorghe Coserea, Jan 01 2018
CROSSREFS
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Sep 27 2010
EXTENSIONS
Terms a(7) and beyond from Gheorghe Coserea, Jan 01 2018
STATUS
approved