A025165 a(n) = H_n(1) / 2^floor(n/2) where H_n is the n-th Hermite polynomial.

1, 2, 1, -2, -5, -2, 23, 58, -103, -670, 257, 7214, 4387, -77794, -134825, 819466, 2841841, -7427774, -55739071, 22221790, 1081264139, 1718092478, -20988454441, -79774943398, 402959508745

Offset: 0

Author

Wouter Meeussen

Keywords

• sign

Links

• G. C. Greubel, Table of n, a(n) for n = 0..800
• Index entries for sequences related to Hermite polynomials

Programs

Magma

[((&+[(-1)^k*Factorial(n)*(2)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]]))/2^(Floor(n/2)): n in [0..30]]; // G. C. Greubel, Jul 10 2018

Maple

A025165 := proc(n)
    HermiteH(n,1)/2^(floor(n/2)) ;
    simplify(%) ;
end proc: # R. J. Mathar, Feb 05 2013

Mathematica

Table[ HermiteH[ n, 1 ]/2^Floor[ n/2 ], {n, 0, 24} ]

PARI

for(n=0,30, print1(polhermite(n,1)/2^(floor(n/2)), ", ")) \\ G. C. Greubel, Jul 10 2018

Formula

a(n) = A062267(n)/A016116(n). - R. J. Mathar, Feb 05 2013

Conjecture: a(n) +a(n-1) +(2*n-5)*a(n-2) +(2*n-7)*a(n-3) +(n-2)*(n-3)*a(n-4) +(n-3)*(n-4)*a(n-5)=0. - R. J. Mathar, Feb 25 2015