A159946 Numerator of Hermite(n, 20/23).

1, 40, 542, -62960, -4238708, 96898400, 26298701320, 436837009600, -177294701591920, -10789176512931200, 1256633088041014240, 164414811028452665600, -8048103437483217101120, -2409334578316563726502400, 14320231546481618948708480, 36259873035884206674901888000

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..385

Formula

From G. C. Greubel, Jul 16 2018: (Start)

a(n) = 23^n * Hermite(n, 20/23).

E.g.f.: exp(40*x - 529*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(40/23)^(n-2*k)/(k!*(n-2*k)!)). (End)

Example

Numerators of 1, 40/23, 542/529, -62960/12167, -4238708/279841, ...

Mathematica

Numerator[Table[HermiteH[n, 20/23], {n, 0, 30}]] (* or *) Table[23^n * HermiteH[n, 20/23], {n, 0, 30}] (* G. C. Greubel, Jul 16 2018 *)

Prog

(PARI) a(n)=numerator(polhermite(n, 20/23)) \\ Charles R Greathouse IV, Jan 29 2016
(PARI) x='x+O('x^30); Vec(serlaplace(exp(40*x - 529*x^2))) \\ G. C. Greubel, Jul 16 2018
(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(40/23)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Jul 16 2018

Crossrefs

Cf. A009967 (denominators).

Sequence in context: A269692 A247409 A107419 * A185744 A374241 A372977

Adjacent sequences: A159943 A159944 A159945 * A159947 A159948 A159949

Keyword

sign,frac

Author

N. J. A. Sloane, Nov 12 2009

Status

approved