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A160083 Numerator of Hermite(n, 23/26). 1
1, 23, 191, -11155, -450239, 4726063, 869603359, 10416421493, -1817903853055, -69977792337337, 3920574297234559, 326698146936593917, -7062637857576430271, -1487528354699082823585, -3179921411888070331681, 6965845981962634303575557, 176336659143413105563860481 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
LINKS
FORMULA
From G. C. Greubel, Sep 23 2018: (Start)
a(n) = 13^n * Hermite(n, 23/26).
E.g.f.: exp(23*x - 169*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(23/13)^(n-2*k)/(k!*(n-2*k)!)). (End)
EXAMPLE
Numerators of 1, 23/13, 191/169, -11155/2197, -450239/28561
MATHEMATICA
HermiteH[Range[0, 20], 23/26]//Numerator (* Harvey P. Dale, Jul 15 2017 *)
Table[13^n*HermiteH[n, 23/26], {n, 0, 30}] (* G. C. Greubel, Sep 23 2018 *)
PROG
(PARI) a(n)=numerator(polhermite(n, 23/26)) \\ Charles R Greathouse IV, Jan 29 2016
(PARI) x='x+O('x^30); Vec(serlaplace(exp(23*x - 169*x^2))) \\ G. C. Greubel, Sep 23 2018
(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(23/13)^(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: A201859 A232150 A269086 * A140545 A062640 A108646
KEYWORD
sign,frac
AUTHOR
N. J. A. Sloane, Nov 12 2009
STATUS
approved

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Last modified April 15 05:45 EDT 2024. Contains 371667 sequences. (Running on oeis4.)