A159659 Numerator of Hermite(n, 7/20).

1, 7, -151, -3857, 63601, 3530807, -38885351, -4509165857, 22875330401, 7374792684007, 10447954066249, -14676449689550257, -125720646772599599, 34343434727512419607, 567277724701345894649, -92190673164125353637057, -2347167886252915159406399

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..442

DLMF Digital library of mathematical functions, Table 18.9.1 for H_n(x)

Formula

D-finite with recurrence a(n) -7*a(n-1) +200*(n-1)*a(n-2)=0. [DLMF] - R. J. Mathar, Feb 16 2014

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

a(n) = 10^n * Hermite(n, 7/20).

E.g.f.: exp(7*x - 100*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(7/10)^(n-2*k)/(k!*(n-2*k)!)). (End)

Example

Numerator of 1, 7/10, -151/100, -3857/1000, 63601/10000, 3530807/100000,...

Maple

A159659 := proc(n)
        orthopoly[H](n, 7/20) ;
        numer(%) ;
end proc: # R. J. Mathar, Feb 16 2014

Mathematica

Numerator[Table[HermiteH[n, 7/20], {n, 0, 30}]] (* Vladimir Joseph Stephan Orlovsky, Jun 16 2011 *)
Table[10^n*HermiteH[n, 7/20], {n, 0, 50}] (* G. C. Greubel, Jul 11 2018 *)

Prog

(PARI) a(n)=numerator(polhermite(n, 7/20)) \\ Charles R Greathouse IV, Jan 29 2016
(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(7/10)^(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. A011557 (denominators)

Sequence in context: A232446 A362491 A202558 * A100868 A171410 A277122

Adjacent sequences: A159656 A159657 A159658 * A159660 A159661 A159662

Keyword

sign,frac

Author

N. J. A. Sloane, Nov 12 2009

Status

approved