This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A342170 #15 Feb 16 2025 08:34:01
%S A342170 1,1,3,33,1485,292545,264168135,1130375449665,23503896724884345,
%T A342170 2422053053602606867905,1256704025339194996874320395,
%U A342170 3326147448057830199712191898815585,45398150793225628820115544929795174823365,3225056167710201318911738099365978237877235350145
%N A342170 Product of first n little Schröder numbers.
%H A342170 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/SuperCatalanNumber.html">Super Catalan Number</a>.
%H A342170 Wikipedia, <a href="http://en.wikipedia.org/wiki/Schr%C3%B6der%E2%80%93Hipparchus_number">Schroeder-Hipparchus numbers</a>.
%F A342170 a(n) = Product_{k=1..n} A001003(k).
%F A342170 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...
%p A342170 b:= proc(n) option remember; `if`(n<2, 1,
%p A342170 ((6*n-3)*b(n-1)-(n-2)*b(n-2))/(n+1))
%p A342170 end:
%p A342170 a:= proc(n) a(n):=`if`(n=0, 1, a(n-1)*b(n)) end:
%p A342170 seq(a(n), n=0..15); # _Alois P. Heinz_, Mar 03 2021
%t A342170 Table[Product[Hypergeometric2F1[1-k, k+2, 2, -1], {k, 1, n}], {n, 0, 15}]
%t A342170 FoldList[Times, 1, Table[Hypergeometric2F1[1 - n, n + 2, 2, -1], {n, 1, 15}]]
%Y A342170 Cf. A001003, A003046, A003266, A070825, A294373, A342166.
%K A342170 nonn
%O A342170 0,3
%A A342170 _Vaclav Kotesovec_, Mar 03 2021