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FORMULA
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Determinant of the n X n matrix in the upper left corner of square table A086620.
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
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MATHEMATICA
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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 *)
Table[Product[Hypergeometric2F1[1/2, -k, 2, -4], {k, 0, n}], {n, 0, 12}] (* Vaclav Kotesovec, Oct 27 2017 *)
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