A159763 Numerator of Hermite(n, 16/21).

1, 32, 142, -51904, -2036660, 117944192, 12755884744, -215972352256, -85665947681648, -1217409408294400, 641059191631501024, 31251445113364640768, -5219510033581154430272, -497789616154448299657216, 43917634328099171108467840, 7552070478774301079638274048

Offset: 0

Author

N. J. A. Sloane, Nov 12 2009

Keywords

• sign
• frac

Links

• Robert Israel, Table of n, a(n) for n = 0..391

Crossrefs

Cf. A009965 (denominators).

Programs

Magma

[Numerator((&+[(-1)^k*Factorial(n)*(32/21)^(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

Maple

seq(21^n*orthopoly[H](n,16/21), n=0..50); # Robert Israel, Jan 02 2018

Mathematica

Numerator[Table[HermiteH[n, 16/21], {n, 0, 30}]] (* Vladimir Joseph Stephan Orlovsky, Jun 17 2011 *)

PARI

a(n)=numerator(polhermite(n, 16/21)) \\ Charles R Greathouse IV, Jan 29 2016

Formula

From Robert Israel, Jan 02 2018: (Start)

a(n) = 21^n * Hermite(n,16/21).

E.g.f.: exp(32*x-441*x^2).

a(n+2) = 32*a(n+1) - 882*(n+1)*a(n). (End)