A160294 Numerator of Hermite(n, 13/30).

1, 13, -281, -15353, 179761, 29972293, -14822441, -81117882833, -1007841787679, 278922434958973, 7707750894566599, -1154950195686012713, -53167719472022830319, 5545550703568171856053, 383123318057719791494839, -29956366297729125403700993

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, 13/30).

E.g.f.: exp(13*x - 225*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(13/15)^(n-2*k)/(k!*(n-2*k)!)). (End)

Example

Numerators of 1, 13/15, -281/225, -15353/3375, 179761/50625, ...

Mathematica

Table[15^n*HermiteH[n, 13/30], {n, 0, 30}] (* G. C. Greubel, Oct 03 2018 *)

Prog

(PARI) a(n)=numerator(polhermite(n, 13/30)) \\ Charles R Greathouse IV, Jan 29 2016
(PARI) x='x+O('x^30); Vec(serlaplace(exp(13*x - 225*x^2))) \\ G. C. Greubel, Oct 03 2018
(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(13/15)^(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: A133284 A012570 A256044 * A092145 A278628 A035017

Adjacent sequences: A160291 A160292 A160293 * A160295 A160296 A160297

Keyword

sign,frac

Author

N. J. A. Sloane, Nov 12 2009

Status

approved