A159806 Numerator of Hermite(n, 1/22).

1, 1, -241, -725, 174241, 876041, -209955569, -1481967101, 354182766785, 3223271074321, -768186794983409, -8568502794840229, 2036344745450994529, 26919276861667019545, -6379421292327161768689, -97581931299655023987149, 23059717359847942196353921

Offset

0,3

Links

G. C. Greubel, Table of n, a(n) for n = 0..434

Formula

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

a(n) = 11^n * Hermite(n, 1/22).

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

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

Example

Numerator of 1, 1/11, -241/121, -725/1331, 174241/14641, ...

Mathematica

Numerator[Table[HermiteH[n, 1/22], {n, 0, 30}]] (* Vladimir Joseph Stephan Orlovsky, Jun 17 2011 *)
Table[11^n*HermiteH[n, 1/22], {n, 0, 50}] (* G. C. Greubel, Jul 11 2018 *)

Prog

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

Crossrefs

Cf. A001020 (denominators).

Sequence in context: A163623 A142856 A204355 * A142452 A167739 A373708

Adjacent sequences: A159803 A159804 A159805 * A159807 A159808 A159809

Keyword

sign,frac

Author

N. J. A. Sloane, Nov 12 2009

Status

approved