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A159654 Numerator of Hermite(n, 16/19). 1
1, 32, 302, -36544, -1823540, 47185792, 8092924744, 54564740864, -39155569948528, -1568144181583360, 204252279714867424, 17858073941907616768, -1050713239354433344832, -188345176292029458712576, 3834948823235768695790720, 2026511404303378366932021248 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..200

FORMULA

Conjecture: a(n) - 32*a(n-1) + 722*(n-1)*a(n-2) = 0. - R. J. Mathar, Feb 16 2014

From G. C. Greubel, Jul 11 2018: (Start)

a(n) = 19^n * Hermite(n, 16/19).

E.g.f.: exp(32*x - 361*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(32/19)^(n-2*k)/(k!*(n-2*k)!)). (End)

EXAMPLE

Numerator of 1, 32/19, 302/361, -36544/6859, -1823540/130321, 47185792/2476099, ...

MAPLE

A159654 := proc(n)

        orthopoly[H](n, 16/19) ;

        numer(%) ;

end proc: # R. J. Mathar, Feb 16 2014

MATHEMATICA

Numerator[Table[HermiteH[n, 16/19], {n, 0, 30}]] (* Vladimir Joseph Stephan Orlovsky, Jun 16 2011 *)

Table[19^n*HermiteH[n, 16/19], {n, 0, 50}] (* G. C. Greubel, Jul 11 2018 *)

PROG

(PARI) a(n)=numerator(polhermite(n, 16/19)) \\ Charles R Greathouse IV, Jan 29 2016

(MAGMA) [Numerator((&+[(-1)^k*Factorial(n)*(32/19)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Jul 11 2018

CROSSREFS

Cf. A001029 (denominators).

Sequence in context: A250563 A060158 A074469 * A061958 A050279 A096764

Adjacent sequences:  A159651 A159652 A159653 * A159655 A159656 A159657

KEYWORD

sign,frac

AUTHOR

N. J. A. Sloane, Nov 12 2009

STATUS

approved

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Last modified October 14 12:45 EDT 2019. Contains 328006 sequences. (Running on oeis4.)