A349068 a(n) = H(n, 2*n), where H(n,x) is n-th Hermite polynomial.
1, 4, 62, 1656, 62476, 3041200, 181253256, 12779289376, 1040259450512, 96008691963456, 9906193528929760, 1129945699713533824, 141183268107518731968, 19176614030629200880384, 2813353012562289110458496, 443345766248682440278848000, 74687922008799389150557901056
Offset: 0
Keywords
Links
- Eric Weisstein's World of Mathematics, Hermite Polynomial.
- Wikipedia, Hermite polynomial.
Programs
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Maple
a:= n-> simplify(HermiteH(n, 2*n)): seq(a(n), n=0..20); # Alois P. Heinz, Nov 07 2021
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Mathematica
Table[HermiteH[n, 2*n], {n, 0, 20}] -
PARI
a(n) = polhermite(n, 2*n); \\ Michel Marcus, Nov 07 2021
Formula
a(n) ~ exp(-1/16) * 4^n * n^n.
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