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A160344 Numerator of Hermite(n, 26/31). 1
1, 52, 782, -159224, -12788660, 559103792, 151972419784, 1454980899424, -1968977929003888, -124758638617745600, 27571931007786483424, 3831601446637967570048, -383682490141447518907712, -108323545252613355018788096, 3953866345538313246451111040 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Harvey P. Dale, Table of n, a(n) for n = 0..369

FORMULA

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)

EXAMPLE

Numerators of 1, 52/31, 782/961, -159224/29791, -12788660/923521, ...

MATHEMATICA

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 *)

PROG

(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

CROSSREFS

Cf. A009975 (denominators).

Sequence in context: A215365 A339142 A264309 * A163691 A007247 A232312

Adjacent sequences:  A160341 A160342 A160343 * A160345 A160346 A160347

KEYWORD

sign,frac

AUTHOR

N. J. A. Sloane, Nov 12 2009

STATUS

approved

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Last modified May 25 01:00 EDT 2022. Contains 354047 sequences. (Running on oeis4.)