A159761 Numerator of Hermite(n, 11/21).

1, 22, -398, -47564, 6700, 167953192, 3665423224, -808168981136, -40410040569968, 4813419438356320, 426670129688245024, -33067616593161351872, -4867041163284902964032, 242912748429751883004544, 61149574443679238811690880, -1654195979849632997482909952

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)*(22/21)^(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, 11/21], {n, 0, 30}]] (* Vladimir Joseph Stephan Orlovsky, Jun 17 2011 *)

PARI

a(n)=numerator(polhermite(n, 11/21)) \\ Charles R Greathouse IV, Jan 29 2016

Formula

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

a(n) = 21^n * Hermite(n,11/21).

E.g.f.: exp(22*x-441*x^2).

a(n) = Sum_{k=0..floor(n/2)} (-1)^k*n!*(22/21)^(n-2k)/(k!*(n-2k)!).

a(n+2) = 22*a(n+1) - 882*(n+1)*a(n). (End)