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A159658
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Numerator of Hermite(n, 3/20).
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1
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1, 3, -191, -1773, 109281, 1746243, -104042271, -2407618413, 138436324161, 4267498433283, -236382888189951, -9244145531135853, 492309917424484641, 23662879026999501123, -1209017148222661563231, -69883112720266587834093, 3417402106507184926190721
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OFFSET
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0,2
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 0..200
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FORMULA
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Conjecture: a(n) -3*a(n-1) +200*(n-1)*a(n-2)=0. - R. J. Mathar, Feb 16 2014
From G. C. Greubel, Jul 11 2018: (Start)
a(n) = 10^n * Hermite(n, 3/20).
E.g.f.: exp(3*x - 100*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(3/10)^(n-2*k)/(k!*(n-2*k)!)). (End)
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EXAMPLE
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Numerator of 1, 3/10, -191/100, -1773/1000, 109281/10000, 1746243/100000..
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MAPLE
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A159658 := proc(n)
orthopoly[H](n, 3/20) ;
numer(%) ;
end proc: # R. J. Mathar, Feb 16 2014
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MATHEMATICA
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Numerator[Table[HermiteH[n, 3/20], {n, 0, 30}]] (* Vladimir Joseph Stephan Orlovsky, Jun 16 2011 *)
Table[10^n*HermiteH[n, 3/20], {n, 0, 50}] (* G. C. Greubel, Jul 11 2018 *)
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PROG
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(PARI) a(n)=numerator(polhermite(n, 3/20)) \\ Charles R Greathouse IV, Jan 29 2016
(MAGMA) [Numerator((&+[(-1)^k*Factorial(n)*(3/10)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Jul 11 2018
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CROSSREFS
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Cf. A011557 (denominators).
Sequence in context: A158469 A261000 A032594 * A257038 A202109 A230171
Adjacent sequences: A159655 A159656 A159657 * A159659 A159660 A159661
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KEYWORD
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sign,frac
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AUTHOR
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N. J. A. Sloane, Nov 12 2009
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STATUS
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approved
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