A160012 Numerator of Hermite(n, 8/25).

1, 16, -994, -55904, 2833036, 324848576, -12508897784, -2636506684544, 67268748657296, 27441366823956736, -317711553211272224, -348100470150839555584, -1201073665758439809344, 5202289873610458296810496, 102754085046341979650807936, -89396007427441548519770753024

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, 8/25).

E.g.f.: exp(16*x - 625*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(16/25)^(n-2*k)/(k!*(n-2*k)!)). (End)

Example

Numerators of 1, 16/25, -994/625, -55904/15625, 2833036/390625

Maple

seq(coeff(series(factorial(n)*exp(16*x-625*x^2), x, n+1), x, n), n=0..15); # Muniru A Asiru, Jul 17 2018

Mathematica

Numerator[HermiteH[Range[0, 20], 8/25]] (* Harvey P. Dale, Sep 29 2013 *)
Table[25^n*HermiteH[n, 8/25], {n, 0, 30}] (* G. C. Greubel, Jul 17 2018 *)

Prog

(PARI) a(n)=numerator(polhermite(n, 8/25)) \\ Charles R Greathouse IV, Jan 29 2016
(PARI) x='x+O('x^30); Vec(serlaplace(exp(16*x - 625*x^2))) \\ G. C. Greubel, Jul 17 2018
(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(16/25)^(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)*(16/25)^(n-2*k)/(Factorial(k)*Factorial(n-2*k)))), NumeratorRat); # Muniru A Asiru, Jul 17 2018

Crossrefs

Cf. A009969 (denominators).

Sequence in context: A181199 A024301 A211090 * A070307 A159683 A197104

Adjacent sequences: A160009 A160010 A160011 * A160013 A160014 A160015

Keyword

sign,frac

Author

N. J. A. Sloane, Nov 12 2009

Status

approved