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A025165
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a(n) = H_n(1) / 2^floor(n/2) where H_n is the n-th Hermite polynomial.
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1
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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
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OFFSET
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0,2
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LINKS
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FORMULA
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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
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MAPLE
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HermiteH(n, 1)/2^(floor(n/2)) ;
simplify(%) ;
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MATHEMATICA
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Table[ HermiteH[ n, 1 ]/2^Floor[ n/2 ], {n, 0, 24} ]
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PROG
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(PARI) for(n=0, 30, print1(polhermite(n, 1)/2^(floor(n/2)), ", ")) \\ G. C. Greubel, Jul 10 2018
(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
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CROSSREFS
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KEYWORD
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sign
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AUTHOR
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STATUS
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approved
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