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A160307
Numerator of Hermite(n, 9/31).
1
1, 18, -1598, -97956, 7450860, 887201208, -55633142856, -11232600902064, 546301487747472, 182545898249590560, -6164096966563140576, -3619485909755267093568, 65170591691483110373568, 84652893673042176232776576, -104600317888637823603991680
OFFSET
0,2
LINKS
FORMULA
From Vincenzo Librandi, Jan 19 2017: (Start)
E.g.f.: exp(18*x - 961*x^2).
a(n+2) = -1922*(n+1)*a(n)+18*a(n+1). (End)
From G. C. Greubel, Oct 04 2018: (Start)
a(n) = 31^n * Hermite(n, 9/31).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(18/31)^(n-2*k)/(k!*(n-2*k)!)). (End)
EXAMPLE
Numerators of 1, 18/31, -1598/961, -97956/29791, 7450860/923521, ...
MATHEMATICA
Numerator[HermiteH[Range[0, 20], 9/31]] (* Harvey P. Dale, Jan 18 2017 *)
Table[31^n*HermiteH[n, 9/31], {n, 0, 30}] (* G. C. Greubel, Oct 04 2018 *)
PROG
(PARI) a(n)=numerator(polhermite(n, 9/31)) \\ Charles R Greathouse IV, Jan 29 2016
(PARI) x='x+O('x^30); Vec(serlaplace(exp(18*x - 961*x^2))) \\ G. C. Greubel, Oct 04 2018
(Sage) [numerator(hermite(n, 9/31)) for n in range(20)] # Bruno Berselli, Jan 19 2017
(Maxima) makelist(num(hermite(n, 9/31)), n, 0, 20); /* Bruno Berselli, Jan 19 2017 */
(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(18/31)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Oct 04 2018
CROSSREFS
Cf. A009975 (denominators).
Sequence in context: A210823 A258336 A211310 * A003030 A276016 A086366
KEYWORD
sign,frac
AUTHOR
N. J. A. Sloane, Nov 12 2009
STATUS
approved