A159826 Numerator of Hermite(n, 7/22).

1, 7, -193, -4739, 106945, 5335967, -92051681, -8392185851, 97190246657, 16927603534135, -93187132480001, -41617110479966707, -43255626698004287, 120553299446937287119, 979955297720482496735, -401574891442180151282027, -6368261970820612522122239

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..435

Formula

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

a(n) = 11^n * Hermite(n, 7/22).

E.g.f.: exp(7*x - 121*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(7/11)^(n-2*k)/(k!*(n-2*k)!)). (End)

Example

Numerators of 1, 7/11, -193/121, -4739/1331, 106945/14641, ...

Mathematica

Numerator[Table[HermiteH[n, 7/22], {n, 0, 30}]] (* Vladimir Joseph Stephan Orlovsky, Jun 17 2011 *)
Table[11^n*HermiteH[n, 7/22], {n, 0, 30}] (* G. C. Greubel, Jul 11 2018 *)

Prog

(PARI) a(n)=numerator(polhermite(n, 7/22)) \\ Charles R Greathouse IV, Jan 29 2016
(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(7/11)^(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. A001020 (denominators).

Sequence in context: A264353 A024096 A030257 * A012849 A308610 A277420

Adjacent sequences: A159823 A159824 A159825 * A159827 A159828 A159829

Keyword

sign,frac

Author

N. J. A. Sloane, Nov 12 2009

Status

approved