A277379 E.g.f.: exp(x/(1-x^2))/sqrt(1-x^2).

1, 1, 2, 10, 40, 296, 1936, 17872, 164480, 1820800, 21442816, 279255296, 3967316992, 59837670400, 988024924160, 17009993230336, 318566665977856, 6177885274406912, 129053377688043520, 2786107670662021120, 64136976817284448256, 1525720008470138454016

Offset: 0

Author

Vladimir Reshetnikov, Oct 11 2016

Keywords

• nonn

Comments

Is this the same as A227545 (at least for n>=1)?

Links

• Eric Weisstein's World of Mathematics, Hermite Polynomial.
• Wikipedia, Hermite polynomials.

Crossrefs

Cf. A000321, A000898, A059343, A062267, A067994, A227545, A277280, A277281, A277378.

Programs

Mathematica

Table[Abs[HermiteH[n, (1 + I)/2]]^2/2^n, {n, 0, 20}]

Formula

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).

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).

a(n) ~ n^n * exp(sqrt(2*n)-n) / 2. - Vaclav Kotesovec, Oct 14 2016