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A160344
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Numerator of Hermite(n, 26/31).
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1
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1, 52, 782, -159224, -12788660, 559103792, 151972419784, 1454980899424, -1968977929003888, -124758638617745600, 27571931007786483424, 3831601446637967570048, -383682490141447518907712, -108323545252613355018788096, 3953866345538313246451111040
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OFFSET
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0,2
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LINKS
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Harvey P. Dale, Table of n, a(n) for n = 0..369
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FORMULA
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From G. C. Greubel, Jul 12 2018: (Start)
a(n) = 31^n * Hermite(n, 26/31).
E.g.f.: exp(52*x - 961*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(52/31)^(n-2*k)/(k!*(n-2*k)!)). (End)
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EXAMPLE
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Numerators of 1, 52/31, 782/961, -159224/29791, -12788660/923521, ...
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MATHEMATICA
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Numerator[HermiteH[Range[0, 20], 26/31]] (* Harvey P. Dale, Jan 26 2016 *)
Table[31^n*HermiteH[n, 26/31], {n, 0, 30}] (* G. C. Greubel, Jul 12 2018 *)
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PROG
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(PARI) a(n)=numerator(polhermite(n, 26/31)) \\ Charles R Greathouse IV, Jan 29 2016
(MAGMA) [Numerator((&+[(-1)^k*Factorial(n)*(52/31)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Jul 12 2018
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CROSSREFS
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Cf. A009975 (denominators).
Sequence in context: A215365 A339142 A264309 * A163691 A007247 A232312
Adjacent sequences: A160341 A160342 A160343 * A160345 A160346 A160347
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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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