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A160292 Numerator of Hermite(n, 7/30). 1
1, 7, -401, -9107, 477601, 19735807, -936451601, -59841840107, 2530929662401, 233147132022007, -8618235208570001, -1109489740559021507, 34893836098508354401, 6235501451708274618607, -160480431014315950915601, -40407022162862341753633307, 800393754206596276404873601 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..412

FORMULA

From G. C. Greubel, Oct 03 2018: (Start)

a(n) = 15^n * Hermite(n, 7/30).

E.g.f.: exp(7*x - 225*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(7/15)^(n-2*k)/(k!*(n-2*k)!)). (End)

EXAMPLE

Numerators of 1, 7/15, -401/225, -9107/3375, 477601/50625, ...

MATHEMATICA

Table[15^n*HermiteH[n, 7/30], {n, 0, 30}] (* G. C. Greubel, Oct 03 2018 *)

PROG

(PARI) a(n)=numerator(polhermite(n, 7/30)) \\ Charles R Greathouse IV, Jan 29 2016

(PARI) x='x+O('x^30); Vec(serlaplace(exp(7*x - 225*x^2))) \\ G. C. Greubel, Oct 03 2018

(MAGMA) [Numerator((&+[(-1)^k*Factorial(n)*(7/15)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Oct 03 2018

CROSSREFS

Cf. A001024 (denominators).

Sequence in context: A203588 A015022 A225167 * A215562 A099125 A172894

Adjacent sequences:  A160289 A160290 A160291 * A160293 A160294 A160295

KEYWORD

sign,frac

AUTHOR

N. J. A. Sloane, Nov 12 2009

STATUS

approved

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Last modified February 18 04:48 EST 2020. Contains 332011 sequences. (Running on oeis4.)