A159762 Numerator of Hermite(n, 13/21).

1, 26, -206, -51220, -786644, 160251416, 7635636856, -649523935216, -64030044264560, 2918259736005536, 584145244508221216, -10551274514355075904, -5941710299591994211136, -42809778329457726121600, 67014596058555904745723776, 2270994640334597525538334976

Offset: 0

Author

N. J. A. Sloane, Nov 12 2009

Keywords

• sign
• frac

Links

• G. C. Greubel, Table of n, a(n) for n = 0..390

Crossrefs

Cf. A009965 (denominators).

Programs

Magma

[Numerator((&+[(-1)^k*Factorial(n)*(26/21)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, May 21 2018

Mathematica

Numerator[Table[HermiteH[n, 13/21], {n, 0, 30}]] (* Vladimir Joseph Stephan Orlovsky, Jun 17 2011 *)

PARI

a(n)=numerator(polhermite(n, 13/21)) \\ Charles R Greathouse IV, Jan 29 2016

Formula

From G. C. Greubel, May 22 2018: (Start)

a(n) = 21^n * Hermite(n,13/21).

E.g.f.: exp(26*x-441*x^2).

a(n) = Sum_{k=0..floor(n/2)} (-1)^k*n!*(26/21)^(n-2k)/(k!*(n-2k)!).

a(n+2) = 26*a(n+1) - 882*(n+1)*a(n). (End)