OFFSET
0,2
LINKS
Eric Weisstein's World of Mathematics, Hermite Polynomial.
Wikipedia, Hermite polynomials.
FORMULA
E.g.f.: exp(2*x/(1-x))/sqrt(1-x^2).
a(n) = |H_n(i)|^2 / 2^n = H_n(i) * H_n(-i) / 2^n, where H_n(x) is n-th Hermite polynomial, i = sqrt(-1).
D-finite with recurrence: (n+2)*(a(n) + n*a(n-1)) = a(n+1) + n*(n-1)^2*a(n-2).
a(n) ~ n^n / (2 * exp(1 - 2*sqrt(2*n) + n)) * (1 + 2*sqrt(2)/(3*sqrt(n))). - Vaclav Kotesovec, Oct 27 2021
MATHEMATICA
Table[Abs[HermiteH[n, I]]^2/2^n, {n, 0, 20}]
With[{nn=20}, CoefficientList[Series[Exp[2x/(1-x)]/Sqrt[1-x^2], {x, 0, nn}], x] Range[ 0, nn]!] (* Harvey P. Dale, Jan 27 2023 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Vladimir Reshetnikov, Oct 11 2016
STATUS
approved