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A159947 Numerator of Hermite(n, 21/23). 1
1, 42, 706, -59220, -4728084, 52039512, 27197223864, 811936580112, -167321303572080, -13899725964095328, 1009444962121341984, 189455789109224933568, -3790777326580730799936, -2564543346247110450176640, -55572469192587267485099136, 35651972338523534753642227968 (list; graph; refs; listen; history; text; internal format)
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

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Last modified September 22 02:48 EDT 2021. Contains 347605 sequences. (Running on oeis4.)