OFFSET
0,2
COMMENTS
It is conjectured that a(n) is always an integer.
If all terms except the first are doubled, we get A324478, which IS known to be integral.
LINKS
N. J. A. Sloane, Table of n, a(n) for n = 0..360
Luis Fredes, Avelio Sepulveda, Tree-decorated planar maps, arXiv:1901.04981 [math.CO], 2019. See Remark 4.6.
FORMULA
a(n+1) = a(n)*4*(4*n+1)*(4*n+2)*(4*n+3)/((n+1)^2*(n+4)) for n>0.
From Vaclav Kotesovec, Jul 21 2019: (Start)
For n>0, a(n) = 3*(4*n)! / ((n!)^3 * (n+3)!).
a(n) ~ 3 * 2^(8*n - 1/2) / (Pi^(3/2) * n^(9/2)). (End)
MATHEMATICA
c[m_, n_] := m Product[1/(n + i), {i, m}] (Multinomial @@ ConstantArray[n, m + 1]); {1}~Join~Array[c[3, #] &, 14] (* Michael De Vlieger, Mar 01 2019 *)
Flatten[{1, Table[3*(4*n)! / ((n!)^3 * (n+3)!), {n, 1, 15}]}] (* Vaclav Kotesovec, Jul 21 2019 *)
PROG
(Magma) [1] cat [n le 1 select 3 else Self(n-1)*4*(4*n-3)*(4*n-2)*(4*n-1)/((n)^2*(n+3)): n in [1..20]]; // Vincenzo Librandi, Mar 11 2019
CROSSREFS
KEYWORD
nonn
AUTHOR
Michael De Vlieger and N. J. A. Sloane, Mar 01 2019
STATUS
approved