A159947 Numerator of Hermite(n, 21/23).

1, 42, 706, -59220, -4728084, 52039512, 27197223864, 811936580112, -167321303572080, -13899725964095328, 1009444962121341984, 189455789109224933568, -3790777326580730799936, -2564543346247110450176640, -55572469192587267485099136, 35651972338523534753642227968

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, 21/23).

E.g.f.: exp(42*x - 529*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(42/23)^(n-2*k)/(k!*(n-2*k)!)). (End)

Example

Numerators of 1, 42/23, 706/529, -59220/12167, -4728084/279841, ...

Mathematica

Numerator[HermiteH[Range[0, 20], 21/23]] (* Harvey P. Dale, Dec 18 2015 *)
Table[23^n * HermiteH[n, 21/23], {n, 0, 30}] (* G. C. Greubel, Jul 16 2018 *)

Prog

(PARI) a(n)=numerator(polhermite(n, 21/23)) \\ Charles R Greathouse IV, Jan 29 2016
(PARI) x='x+O('x^30); Vec(serlaplace(exp(42*x - 529*x^2))) \\ G. C. Greubel, Jul 16 2018
(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(42/23)^(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: A007746 A200853 A214945 * A330845 A333113 A252827

Adjacent sequences: A159944 A159945 A159946 * A159948 A159949 A159950

Keyword

sign,frac

Author

N. J. A. Sloane, Nov 12 2009

Status

approved