A349068 - OEIS

%I #19 Nov 07 2021 14:16:44

%S 1,4,62,1656,62476,3041200,181253256,12779289376,1040259450512,

%T 96008691963456,9906193528929760,1129945699713533824,

%U 141183268107518731968,19176614030629200880384,2813353012562289110458496,443345766248682440278848000,74687922008799389150557901056

%N a(n) = H(n, 2*n), where H(n,x) is n-th Hermite polynomial.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/HermitePolynomial.html">Hermite Polynomial</a>.

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Hermite_polynomials">Hermite polynomial</a>.

%F a(n) ~ exp(-1/16) * 4^n * n^n.

%F a(n) = Sum_{k=0..floor(n/2)} (-1)^k * ( n! / (k! * (n-2k)!) ) * (4n)^(n-2k), for n>0. - _Bernard Schott_, Nov 07 2021

%p a:= n-> simplify(HermiteH(n, 2*n)):

%p seq(a(n), n=0..20);  # _Alois P. Heinz_, Nov 07 2021

%t Table[HermiteH[n, 2*n], {n, 0, 20}]

%o (PARI) a(n) =  polhermite(n, 2*n); \\ _Michel Marcus_, Nov 07 2021

%Y Cf. A285270, A349066, A349069.

%K nonn

%O 0,2

%A _Vaclav Kotesovec_, Nov 07 2021