A160037 Numerator of Hermite(n, 11/25).

1, 22, -766, -71852, 1291756, 387678632, 455454904, -2897569732112, -67731764516464, 27485598501757792, 1366665517848891424, -313503339879296788672, -25688724347766786430784, 4137398162538582528602752, 508464530227059095129500544, -61218248179429894157699148032

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, 11/25).

E.g.f.: exp(22*x - 625*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(22/25)^(n-2*k)/(k!*(n-2*k)!)). (End)

Example

Numerators of 1, 22/25, -766/625, -71852/15625, 1291756/390625, ...

Maple

seq(coeff(series(factorial(n)*exp(22*x-625*x^2), x, n+1), x, n), n=0..15); # Muniru A Asiru, Jul 17 2018

Mathematica

Numerator[HermiteH[Range[0, 20], 11/25]] (* Harvey P. Dale, Dec 27 2011 *)
Table[25^n* HermiteH[n, 11/25], {n, 0, 30}] (* G. C. Greubel, Jul 17 2018 *)

Prog

(PARI) a(n)=numerator(polhermite(n, 11/25)) \\ Charles R Greathouse IV, Jan 29 2016
(PARI) x='x+O('x^30); Vec(serlaplace(exp(22*x - 625*x^2))) \\ G. C. Greubel, Jul 17 2018
(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(22/25)^(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)*(22/25)^(n-2*k)/(Factorial(k)*Factorial(n-2*k)))), NumeratorRat); # Muniru A Asiru, Jul 17 2018

Crossrefs

Cf. A009969 (denominators).

Sequence in context: A159189 A067768 A181181 * A278440 A152957 A237605

Adjacent sequences: A160034 A160035 A160036 * A160038 A160039 A160040

Keyword

sign,frac

Author

N. J. A. Sloane, Nov 12 2009

Status

approved