A159948 Numerator of Hermite(n, 22/23).

1, 44, 878, -54472, -5183540, 2449744, 27528715336, 1195712499872, -151266315784048, -16776228493414720, 702203805185457376, 208389464888487862144, 996888570345112992448, -2601849549129056926112512, -128192585558205188847080320, 32898121757138562880306993664

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..385

Formula

From G. C. Greubel, Jul 16 2018: (Start)

a(n) = 23^n * Hermite(n, 22/23).

E.g.f.: exp(44*x - 529*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(44/23)^(n-2*k)/(k!*(n-2*k)!)). (End)

Example

Numerators of 1, 44/23, 878/529, -54472/12167, -5183540/279841, ...

Mathematica

Numerator[Table[HermiteH[n, 22/23], {n, 0, 30}]] (* or *) Table[23^n * HermiteH[n, 22/23], {n, 0, 30}] (* G. C. Greubel, Jul 16 2018 *)

Prog

(PARI) a(n)=numerator(polhermite(n, 22/23)) \\ Charles R Greathouse IV, Jan 29 2016
(PARI) x='x+O('x^30); Vec(serlaplace(exp(44*x - 529*x^2))) \\ G. C. Greubel, Jul 16 2018
(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(44/23)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Jul 16 2018

Crossrefs

Cf. A009967 (denominators).

Sequence in context: A282994 A295273 A244998 * A183756 A183750 A133349

Adjacent sequences: A159945 A159946 A159947 * A159949 A159950 A159951

Keyword

sign,frac

Author

N. J. A. Sloane, Nov 12 2009

Status

approved