OFFSET
0,3
LINKS
Eric Weisstein's World of Mathematics, Motzkin Number.
FORMULA
a(n) = Product_{k=1..n} A001006(k).
a(n) ~ c * 3^(n*(n+4)/2) * exp(3*n/2) / (2^(n + 3/4) * Pi^(n/2 + 3/4) * n^(3*n/2 + 51/16)), where c = 1.88710807429950713889649869555827071385924787813206239984338608598135477864...
MAPLE
b:= proc(n) option remember; `if`(n<2, 1,
((2*n+1)*b(n-1) +(3*n-3)*b(n-2))/(n+2))
end:
a:= proc(n) a(n):=`if`(n=0, 1, a(n-1)*b(n)) end:
seq(a(n), n=0..18); # Alois P. Heinz, Mar 04 2021
MATHEMATICA
Table[Product[Hypergeometric2F1[(1-k)/2, -k/2, 2, 4], {k, 1, n}], {n, 0, 15}]
FoldList[Times, 1, Table[Hypergeometric2F1[(1 - n)/2, -n/2, 2, 4], {n, 1, 15}]]
CROSSREFS
KEYWORD
nonn
AUTHOR
Vaclav Kotesovec, Mar 04 2021
STATUS
approved