A160003 Numerator of Hermite(n, 1/25).

1, 2, -1246, -7492, 4657516, 46775032, -29015924936, -408844589872, 253071654010256, 4594589206740512, -2837866929201898976, -63108098942660197952, 38894454078640790524096, 1024410392297184550328192, -629986057993318476915903616, -19187153981187366584575167232

Offset

0,2

Links

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

Formula

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

a(n) = 25^n * Hermite(n, 1/25).

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

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

Example

Numerators of 1, 2/25, -1246/625, -7492/15625, 4657516/390625, ...

Mathematica

Numerator[Table[HermiteH[n, 1/25], {n, 0, 30}]] (* or *) Table[25^n* HermiteH[n, 1/25], {n, 0, 30}] (* G. C. Greubel, Jul 16 2018 *)

Prog

(PARI) a(n)=numerator(polhermite(n, 1/25)) \\ Charles R Greathouse IV, Jan 29 2016
(PARI) x='x+O('x^30); Vec(serlaplace(exp(2*x - 625*x^2))) \\ G. C. Greubel, Jul 16 2018
(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(2/25)^(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. A009969 (denominators).

Sequence in context: A281250 A369777 A171940 * A374793 A078170 A062663

Adjacent sequences: A160000 A160001 A160002 * A160004 A160005 A160006

Keyword

sign,frac

Author

N. J. A. Sloane, Nov 12 2009

Status

approved