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A160061 Numerator of Hermite(n, 16/25). 1
1, 32, -226, -87232, -1943924, 373954432, 24116066824, -2032944101632, -276069795962224, 11495207545528832, 3473631846031942624, -32533875246088236032, -48803521890814034633024, -1073704571814725567776768, 758698684427656844617783424, 43068187908442716463862509568 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..380

FORMULA

From G. C. Greubel, Sep 23 2018: (Start)

a(n) = 25^n * Hermite(n, 16/25).

E.g.f.: exp(32*x - 625*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(32/25)^(n-2*k)/(k!*(n-2*k)!)). (End)

EXAMPLE

Numerators of 1, 32/25, -226/625, -87232/15625, -1943924/390625, ...

MATHEMATICA

Numerator[Table[HermiteH[n, 16/25], {n, 0, 50}]] (* G. C. Greubel, Sep 23 2018 *)

PROG

(PARI) a(n)=numerator(polhermite(n, 16/25)) \\ Charles R Greathouse IV, Jan 29 2016

(PARI) x='x+O('x^30); Vec(serlaplace(exp(32*x - 625*x^2))) \\ G. C. Greubel, Sep 23 2018

(MAGMA) [Numerator((&+[(-1)^k*Factorial(n)*(32/25)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Sep 23 2018

CROSSREFS

Cf. A009969 (denominators).

Sequence in context: A250232 A070053 A022146 * A269585 A199913 A301795

Adjacent sequences:  A160058 A160059 A160060 * A160062 A160063 A160064

KEYWORD

sign,frac

AUTHOR

N. J. A. Sloane, Nov 12 2009

STATUS

approved

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Last modified January 20 05:55 EST 2021. Contains 340301 sequences. (Running on oeis4.)