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%I #10 Oct 27 2017 11:54:45
%S 1,2,10,150,7650,1438200,1051324200,3101406390000,37945707181650000,
%T 1966422437567466300000,438887790263120370963300000,
%U 427664112802721593716655529100000
%N Product of first n terms of the binomial transform of the Catalan numbers (A007317).
%H Vaclav Kotesovec, <a href="/A086619/b086619.txt">Table of n, a(n) for n = 0..56</a>
%F Determinant of the n X n matrix in the upper left corner of square table A086620.
%F a(n) ~ c * 5^(n*(n+4)/2) * exp(3*n/2) / (2^(3*n) * Pi^(n/2) * n^(3*n/2 + 27/16)), where c = 0.286457028871544332017553737430712054187435533562040177617845850168... - _Vaclav Kotesovec_, Oct 27 2017
%t Table[Product[Sum[Binomial[m, k]*Binomial[2*k, k]/(k+1), {k, 0, m}], {m, 0, n}], {n, 0, 12}] (* _Vaclav Kotesovec_, Oct 27 2017 *)
%t Table[Product[Hypergeometric2F1[1/2, -k, 2, -4], {k, 0, n}], {n, 0, 12}] (* _Vaclav Kotesovec_, Oct 27 2017 *)
%Y Cf. A007317, A003046, A086620.
%K nonn
%O 0,2
%A _Paul D. Hanna_, Jul 24 2003
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