A159883 Numerator of Hermite(n, 14/23).

1, 28, -274, -66920, -1004084, 255091088, 12454154824, -1270601891552, -127812323590000, 7175629349576128, 1417946567012111584, -36215654642176309888, -17516100476867891291456, -30656862015230525822720, 240058053822414522099649664, 7175714947197201167276319232

Offset: 0

Author

N. J. A. Sloane, Nov 12 2009

Keywords

• sign
• frac

Examples

			Numerators of 1, 28/23, -274/529, -66920/12167, -1004084/279841, ...
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..390
• DLMF Digital library of mathematical functions, Table 18.9.1 for H_n(x)
• Simon Plouffe, Conjectures of the OEIS, as of June 20, 2018.

Crossrefs

Cf. A009967 (denominators).

Programs

GAP

List(List([0..20],n->Sum([0..Int(n/2)],k->(-1)^k*Factorial(n)*(28/23)^(n-2*k)/(Factorial(k)*Factorial(n-2*k)))),NumeratorRat); # Muniru A Asiru, Jul 12 2018

Magma

[Numerator((&+[(-1)^k*Factorial(n)*(28/23)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..20]]; // Vincenzo Librandi, Jun 23 2018

Mathematica

Numerator[Table[HermiteH[n, 14/23], {n, 0, 40}]] (* Vincenzo Librandi, Jun 23 2018 *)
Table[23^n*HermiteH[n, 14/23], {n,0,30}] (* G. C. Greubel, Jul 11 2018 *)

PARI

a(n)=numerator(polhermite(n, 14/23)) \\ Charles R Greathouse IV, Jan 29 2016

PARI

x='x+O('x^99); Vec(serlaplace(exp(-529*x^2+28*x))) \\ Altug Alkan, Jul 30 2018

Formula

E.g.f.: exp(-529*x^2 + 28*x). - Simon Plouffe, Jun 22 2018; corrected by G. C. Greubel, Jul 11 2018

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

a(n) = 23^n * Hermite(n, 14/23).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(28/23)^(n-2*k)/(k!*(n-2*k)!)). (End)

D-finite with recurrence a(n) -28*a(n-1) +1058*(n-1)*a(n-2)=0. [DLMF] - R. J. Mathar, Feb 06 2021