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A160063 Numerator of Hermite(n, 18/25). 1
1, 36, 46, -88344, -3352884, 321016176, 32512107336, -1237185455904, -329019615602544, 527148397348416, 3720448017833162976, 127346773675138667136, -46571676392900998903104, -3586781955271515967551744, 627665590994866657343577216, 85364645493066729096524299776 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..380

FORMULA

From G. C. Greubel, Sep 23 2018: (Start)

a(n) = 25^n * Hermite(n, 18/25).

E.g.f.: exp(36*x - 625*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(36/25)^(n-2*k)/(k!*(n-2*k)!)). (End)

EXAMPLE

Numerators of 1, 36/25, 46/625, -88344/15625, -3352884/390625, ...

MATHEMATICA

Numerator[HermiteH[Range[0, 20], 18/25]] (* Harvey P. Dale, Mar 18 2015 *)

Table[25^n*HermiteH[n, 18/25], {n, 0, 30}] (* G. C. Greubel, Sep 23 2018 *)

PROG

(PARI) a(n)=numerator(polhermite(n, 18/25)) \\ Charles R Greathouse IV, Jan 29 2016

(PARI) x='x+O('x^30); Vec(serlaplace(exp(36*x - 625*x^2))) \\ G. C. Greubel, Sep 23 2018

(MAGMA) [Numerator((&+[(-1)^k*Factorial(n)*(36/25)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Sep 23 2018

CROSSREFS

Cf. A009969 (denominators).

Sequence in context: A188630 A167310 A083674 * A260927 A291713 A287840

Adjacent sequences:  A160060 A160061 A160062 * A160064 A160065 A160066

KEYWORD

sign,frac

AUTHOR

N. J. A. Sloane, Nov 12 2009

STATUS

approved

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Last modified November 26 16:27 EST 2020. Contains 338641 sequences. (Running on oeis4.)