A160291 Numerator of Hermite(n, 1/30).

1, 1, -449, -1349, 604801, 3033001, -1357769249, -9546871949, 4267426262401, 38636165278801, -17244440197445249, -191107183952049749, 85168871793401932801, 1117147665134470577401, -497120752326266836308449, -7535151042673431473934749, 3348029927159627713608096001

Offset

0,3

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, 1/30).

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

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

Example

Numerators of 1, 1/15, -449/225, -1349/3375, 604801/50625, ...

Mathematica

Table[15^n*HermiteH[n, 1/30], {n, 0, 30}] (* G. C. Greubel, Oct 03 2018 *)

Prog

(PARI) a(n)=numerator(polhermite(n, 1/30)) \\ Charles R Greathouse IV, Jan 29 2016
(PARI) x='x+O('x^30); Vec(serlaplace(exp(x - 225*x^2))) \\ G. C. Greubel, Oct 03 2018
(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(1/15)^(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: A325083 A243402 A135073 * A193255 A283791 A036945

Adjacent sequences: A160288 A160289 A160290 * A160292 A160293 A160294

Keyword

sign,frac

Author

N. J. A. Sloane, Nov 12 2009

Status

approved