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A160307
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Numerator of Hermite(n, 9/31).
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1
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1, 18, -1598, -97956, 7450860, 887201208, -55633142856, -11232600902064, 546301487747472, 182545898249590560, -6164096966563140576, -3619485909755267093568, 65170591691483110373568, 84652893673042176232776576, -104600317888637823603991680
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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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E.g.f.: exp(18*x - 961*x^2).
a(n+2) = -1922*(n+1)*a(n)+18*a(n+1). (End)
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)
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EXAMPLE
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Numerators of 1, 18/31, -1598/961, -97956/29791, 7450860/923521, ...
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MATHEMATICA
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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 *)
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PROG
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(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
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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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