A160005 Numerator of Hermite(n, 3/25).

1, 6, -1214, -22284, 4418796, 137932776, -26789878344, -1195235090064, 227240024969616, 13315791050457696, -2476555534605433824, -181306721338353802944, 32964798272794592262336, 2917389609712074597734016, -518173634274639676676555904, -54163359975609143520404615424

Offset

0,2

Links

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

Formula

From G. C. Greubel, Jul 17 2018: (Start)

a(n) = 25^n * Hermite(n, 3/25).

E.g.f.: exp(6*x - 625*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(6/25)^(n-2*k)/(k!*(n-2*k)!)). (End)

Example

Numerators of 1, 6/25, -1214/625, -22284/15625, 4418796/390625, ...

Maple

seq(coeff(series(factorial(n)*exp(6*x-625*x^2), x, n+1), x, n), n=0..15); # Muniru A Asiru, Jul 17 2018

Mathematica

Numerator[Table[HermiteH[n, 3/25], {n, 0, 30}]] (* or *) Table[25^n* HermiteH[n, 3/25], {n, 0, 30}] (* G. C. Greubel, Jul 17 2018 *)

Prog

(PARI) a(n)=numerator(polhermite(n, 3/25)) \\ Charles R Greathouse IV, Jan 29 2016
(PARI) x='x+O('x^30); Vec(serlaplace(exp(6*x - 625*x^2))) \\ G. C. Greubel, Jul 17 2018
(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(6/25)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Jul 17 2018
(GAP) List(List([0..15], n->Sum([0..Int(n/2)], k->(-1)^k*Factorial(n)*(6/25)^(n-2*k)/(Factorial(k)*Factorial(n-2*k)))), NumeratorRat); # Muniru A Asiru, Jul 17 2018

Crossrefs

Cf. A009969 (denominators).

Sequence in context: A113159 A159717 A160857 * A172923 A131675 A263437

Adjacent sequences: A160002 A160003 A160004 * A160006 A160007 A160008

Keyword

sign,frac

Author

N. J. A. Sloane, Nov 12 2009

Status

approved