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%I #10 Jan 05 2021 21:58:02
%S 1,2,9,36,225,1350,11025,88200,893025,8930250,108056025,1296672300,
%T 18261468225,255660555150,4108830350625,65741285610000,
%U 1187451971330625,21374135483951250,428670161650355625,8573403233007112500
%N Exponential (binomial) convolution of A001818 (with interspersed zeros) and A000142 (factorials).
%F E.g.f.: (1/sqrt(1-x^2))*x/(1-x).
%F a(n) = n!*Sum_{k=0..floor((n-1)/2)} binomial(2*k, k)/(4^k).
%F a(2*k+1) = A111595(2*k+2, 0)= ((2*k+1)!!)^2 = A001818(k+1), k >= 0.
%F a(n) = (n+1)/(n^2)*a(n-1) + (n+1)/(n-1)*a(n-2); a(0)=1, a(1)=2. - _Sergei N. Gladkovskii_, Jul 27 2012
%Y Second column (m=1) of triangle |A111595|.
%K nonn,easy
%O 1,2
%A _Wolfdieter Lang_, Aug 23 2005