A160038 Numerator of Hermite(n, 12/25).

1, 24, -674, -76176, 699276, 397662624, 5173427976, -2858307408576, -113866872595824, 25850269143460224, 1901408776146065376, -277494553665747230976, -32804239959986332463424, 3375116545946536485517824, 614071696452494778183067776, -44326818839204513820168293376

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, 12/25).

E.g.f.: exp(24*x - 625*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(24/25)^(n-2*k)/(k!*(n-2*k)!)). (End)

Example

Numerators of 1, 24/25, -674/625, -76176/15625, 699276/390625

Maple

seq(coeff(series(factorial(n)*exp(24*x-625*x^2), x, n+1), x, n), n=0..15); # Muniru A Asiru, Jul 17 2018

Mathematica

Numerator[Table[HermiteH[n, 12/25], {n, 0, 30}]] (* or *) Table[25^n* HermiteH[n, 12/25], {n, 0, 30}] (* G. C. Greubel, Jul 17 2018 *)

Prog

(PARI) a(n)=numerator(polhermite(n, 12/25)) \\ Charles R Greathouse IV, Jan 29 2016
(PARI) x='x+O('x^30); Vec(serlaplace(exp(24*x - 625*x^2))) \\ G. C. Greubel, Jul 17 2018
(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(24/25)^(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)*(24/25)^(n-2*k)/(Factorial(k)*Factorial(n-2*k)))), NumeratorRat); # Muniru A Asiru, Jul 17 2018

Crossrefs

Cf. A009969 (denominators).

Sequence in context: A268473 A367331 A291066 * A322746 A367330 A184274

Adjacent sequences: A160035 A160036 A160037 * A160039 A160040 A160041

Keyword

sign,frac

Author

N. J. A. Sloane, Nov 12 2009

Status

approved