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A158958
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Numerator of Hermite(n, 3/4).
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1
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1, 3, 1, -45, -159, 963, 9249, -18477, -573375, -537597, 39670209, 162018387, -3004923231, -24568534845, 238806411489, 3468095137107, -18252483967359, -498673629451773, 986316931205505, 74767953434671827, 74383686760778721, -11739721489265156157
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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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D-finite with recurrence a(n) - 3*a(n-1) + 8*(n-1)*a(n-2) = 0. [DLMF] - R. J. Mathar, Feb 16 2014
a(n) = 2^n * Hermite(n, 3/4).
E.g.f.: exp(3*x - 4*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(3/2)^(n-2*k)/(k!*(n-2*k)!)). (End)
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EXAMPLE
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Numerator of 1, 3/2, 1/4, -45/8, -159/16, 963/32, 9249/64, -18477/128, -573375/256, ...
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MAPLE
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orthopoly[H](n, 3/4) ;
numer(%) ;
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MATHEMATICA
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Table[2^n*HermiteH[n, 3/4], {n, 0, 50}] (* G. C. Greubel, Jul 10 2018 *)
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PROG
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(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(3/2)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..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,frac
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AUTHOR
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STATUS
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approved
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