OFFSET
0,2
COMMENTS
Combinatorial interpretation welcome.
Could involve planar maps, lattice walks, interpretations of catalan numbers.
LINKS
Indranil Ghosh, Table of n, a(n) for n = 0..800
H. Franzen, T. Weist, The Value of the Kac Polynomial at One, arXiv preprint arXiv:1608.03419 [math.RT], 2016.
FORMULA
D-finite with recurrence n*(n+3)*a(n) -4*(2*n-1)*(2*n+1)*a(n-1)=0. - R. J. Mathar, Jun 17 2016
MATHEMATICA
CoefficientList[
Series[HypergeometricPFQ[{1/2, 3/2}, {4}, 16*x], {x, 0, 20}], x]
Table[3 CatalanNumber[n] CatalanNumber[n+1] * (n+1) / (n+3), {n, 0, 20}] (* Indranil Ghosh, Mar 05 2017 *)
PROG
(PARI)
c(n) = binomial(2*n, n) / (n+1);
a(n) = 3 * c(n) * c(n+1) *(n+1) / (n+3); \\ Indranil Ghosh, Mar 05 2017
(Python)
import math
f=math.factorial
def C(n, r): return f(n) / f(r) / f(n-r)
def Catalan(n): return C(2*n, n) / (n+1)
def A186266(n): return 3 * Catalan(n) * Catalan(n+1) * (n+1) / (n+3) # Indranil Ghosh, Mar 05 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Olivier Gérard, Feb 16 2011
STATUS
approved