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A160312 Numerator of Hermite(n, 14/31). 1
1, 28, -1138, -139496, 2655820, 1146808208, 6588199624, -13040522665184, -453772272366448, 187805452873608640, 13107905447855859424, -3242599451690793996928, -367920121625910811856192, 64485550348270970013174016, 10998447568696594705407685760 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..368

FORMULA

From G. C. Greubel, Oct 04 2018: (Start)

a(n) = 31^n * Hermite(n, 14/31).

a(n+2) = 28*a(n+1) - 1922*(n+1)*a(n)

E.g.f.: exp(28*x - 961*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(28/31)^(n-2*k)/(k!*(n-2*k)!)). (End)

EXAMPLE

Numerators of 1, 28/31, -1138/961, -139496/29791, 2655820/923521, ...

MATHEMATICA

Table[31^n*HermiteH[n, 14/31], {n, 0, 30}] (* G. C. Greubel, Oct 04 2018 *)

PROG

(PARI) a(n)=numerator(polhermite(n, 14/31)) \\ Charles R Greathouse IV, Jan 29 2016

(PARI) x='x+O('x^30); Vec(serlaplace(exp(28*x - 961*x^2))) \\ G. C. Greubel, Oct 04 2018

(MAGMA) [Numerator((&+[(-1)^k*Factorial(n)*(28/31)^(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: A218480 A162006 A025753 * A132503 A092705 A061321

Adjacent sequences:  A160309 A160310 A160311 * A160313 A160314 A160315

KEYWORD

sign,frac

AUTHOR

N. J. A. Sloane, Nov 12 2009

STATUS

approved

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Last modified October 16 17:25 EDT 2021. Contains 348042 sequences. (Running on oeis4.)