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%I #26 Nov 07 2021 08:04:55
%S 1,2,14,180,3340,80600,2389704,83965616,3409634960,157077960480,
%T 8093278209760,461113571640128,28784033772836544,1953535902100115840,
%U 143219579014652040320,11279408109860685024000,949705205977314865582336,85131076752851318807814656,8094279370190580822082014720
%N a(n) = H_n(n), where H_n is the physicist's n-th Hermite polynomial.
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Hermite_polynomials">Hermite polynomial</a>
%F a(n) ~ exp(-1/4) * 2^n * n^n. - _Vaclav Kotesovec_, Nov 07 2021
%e Knowing that H_3(x) = 8x^3-12x, a(3) = H_3(3) = 8*3^3-12*3 = 180.
%t Table[HermiteH[n, n], {n, 0, 18}] (* _Michael De Vlieger_, May 25 2017 *)
%o (PARI) a(n) = polhermite(n, n); \\ _Michel Marcus_, May 25 2017
%o (Python)
%o from sympy import hermite
%o def a(n): return hermite(n, n) # _Indranil Ghosh_, May 25 2017
%Y Cf. A089466 (probabilist's variant).
%Y Cf. A349066, A349067, A349068, A349069.
%K nonn
%O 0,2
%A _Natan Arie Consigli_, May 24 2017
%E More terms from _Michel Marcus_, May 25 2017
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