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%I #5 May 24 2023 07:33:17
%S 1,2,12,86,816,9126,122028,1855802,32001504,613558458,12989299596,
%T 300515004558,7550646317520,204680035934550,5955892801274796,
%U 185157207502788074,6125200081143892800,214837212308039658666,7963817560398871790604,311101097650387613661510
%N Product_{n>=1} 1 / (1 - a(n)*x^n) = 1 + 1!!*x + 3!!*x^2 + 5!!*x^3 + 7!!*x^4 + ...
%t A[m_, n_] := A[m, n] = Which[m == 1, (2 n - 1)!!, m > n >= 1, 0, True, A[m - 1, n] - A[m - 1, m - 1] A[m - 1, n - m + 1]]; a[n_] := A[n, n]; a /@ Range[1, 20]
%Y Cf. A001147, A305868, A305870, A316084, A363254.
%K nonn
%O 1,2
%A _Ilya Gutkovskiy_, May 23 2023