OFFSET
0,3
LINKS
Eric Weisstein's World of Mathematics, Super Catalan Number.
Wikipedia, Schroeder-Hipparchus numbers.
FORMULA
a(n) = Product_{k=1..n} A001003(k).
a(n) ~ c * (1 + sqrt(2))^(n*(n+2)) * exp(3*n/2) / (2^((7*n + 3)/4) * Pi^((2*n + 3)/4) * n^(3*n/2 + 3/2 + 9/(16*sqrt(2)))), where c = 0.89405100528141459535141257102427907468205556782800836208733677564241771912...
MAPLE
b:= proc(n) option remember; `if`(n<2, 1,
((6*n-3)*b(n-1)-(n-2)*b(n-2))/(n+1))
end:
a:= proc(n) a(n):=`if`(n=0, 1, a(n-1)*b(n)) end:
seq(a(n), n=0..15); # Alois P. Heinz, Mar 03 2021
MATHEMATICA
Table[Product[Hypergeometric2F1[1-k, k+2, 2, -1], {k, 1, n}], {n, 0, 15}]
FoldList[Times, 1, Table[Hypergeometric2F1[1 - n, n + 2, 2, -1], {n, 1, 15}]]
CROSSREFS
KEYWORD
nonn
AUTHOR
Vaclav Kotesovec, Mar 03 2021
STATUS
approved