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A160012 Numerator of Hermite(n, 8/25). 1
1, 16, -994, -55904, 2833036, 324848576, -12508897784, -2636506684544, 67268748657296, 27441366823956736, -317711553211272224, -348100470150839555584, -1201073665758439809344, 5202289873610458296810496, 102754085046341979650807936, -89396007427441548519770753024 (list; graph; refs; listen; history; text; internal format)
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

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Last modified April 19 13:00 EDT 2021. Contains 343114 sequences. (Running on oeis4.)