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A160073 Numerator of Hermite(n, 9/26). 1
1, 9, -257, -8397, 185025, 13017969, -195530529, -28160215893, 209183288577, 78027873371865, 65915296495551, -263140974328443741, -2613341841326452287, 1043779715304229742913, 20877041488526499035295, -4751272239422876652146661, -148608050501635239978265599 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..422

FORMULA

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

a(n) = 13^n * Hermite(n, 9/26).

E.g.f.: exp(9*x - 169*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(9/13)^(n-2*k)/(k!*(n-2*k)!)). (End)

EXAMPLE

Numerators of 1, 9/13, -257/169, -8397/2197, 185025/28561

MATHEMATICA

Numerator[HermiteH[Range[0, 20], 9/26]] (* Harvey P. Dale, Jul 18 2015 *)

Table[13^n*HermiteH[n, 9/26], {n, 0, 30}] (* G. C. Greubel, Sep 23 2018 *)

PROG

(PARI) a(n)=numerator(polhermite(n, 9/26)) \\ Charles R Greathouse IV, Jan 29 2016

(PARI) x='x+O('x^30); Vec(serlaplace(exp(9*x - 169*x^2))) \\ G. C. Greubel, Sep 23 2018

(MAGMA) [Numerator((&+[(-1)^k*Factorial(n)*(9/13)^(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. A001022 (denominators).

Sequence in context: A193129 A183493 A183424 * A157575 A072158 A001823

Adjacent sequences:  A160070 A160071 A160072 * A160074 A160075 A160076

KEYWORD

sign,frac

AUTHOR

N. J. A. Sloane, Nov 12 2009

STATUS

approved

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Last modified May 20 12:33 EDT 2019. Contains 323422 sequences. (Running on oeis4.)