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%I #16 Jan 30 2020 21:29:17
%S 1,1,2,10,40,296,1936,17872,164480,1820800,21442816,279255296,
%T 3967316992,59837670400,988024924160,17009993230336,318566665977856,
%U 6177885274406912,129053377688043520,2786107670662021120,64136976817284448256,1525720008470138454016
%N E.g.f.: exp(x/(1-x^2))/sqrt(1-x^2).
%C Is this the same as A227545 (at least for n>=1)?
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/HermitePolynomial.html">Hermite Polynomial</a>.
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Hermite_polynomials">Hermite polynomials</a>.
%F a(n) = |H_n((1+i)/2)|^2 / 2^n = H_n((1+i)/2) * H_n((1-i)/2) / 2^n, where H_n(x) is n-th Hermite polynomial, i = sqrt(-1).
%F D-finite with recurrence: (n+1)*(n+2)*(a(n) - n^2*a(n-1)) + (2*n^2+7*n+6)*a(n+1) + a(n+2) = a(n+3).
%F a(n) ~ n^n * exp(sqrt(2*n)-n) / 2. - _Vaclav Kotesovec_, Oct 14 2016
%t Table[Abs[HermiteH[n, (1 + I)/2]]^2/2^n, {n, 0, 20}]
%Y Cf. A000321, A000898, A059343, A062267, A067994, A227545, A277280, A277281, A277378.
%K nonn
%O 0,3
%A _Vladimir Reshetnikov_, Oct 11 2016
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