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#11 by Charles R Greathouse IV at Thu Sep 08 08:45:44 EDT 2022
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| PROG
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(MAGMAMagma) [Numerator((&+[(-1)^k*Factorial(n)*(26/27)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Sep 24 2018
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Discussion
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| Thu Sep 08
| 08:45
| OEIS Server: https://oeis.org/edit/global/2944
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#10 by Bruno Berselli at Tue Sep 25 03:58:13 EDT 2018
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#9 by Michel Marcus at Tue Sep 25 01:50:40 EDT 2018
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#8 by G. C. Greubel at Mon Sep 24 23:37:56 EDT 2018
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#7 by G. C. Greubel at Mon Sep 24 23:37:50 EDT 2018
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| LINKS
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G. C. Greubel, <a href="/A160140/b160140.txt">Table of n, a(n) for n = 0..376</a>
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| FORMULA
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From G. C. Greubel, Sep 24 2018: (Start)
a(n) = 27^n * Hermite(n, 13/27).
E.g.f.: exp(26*x - 729*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(26/27)^(n-2*k)/(k!*(n-2*k)!)). (End)
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| MATHEMATICA
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Table[27^n*HermiteH[n, 13/27], {n, 0, 30}] (* G. C. Greubel, Sep 24 2018 *)
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| PROG
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(PARI) x='x+O('x^30); Vec(serlaplace(exp(26*x - 729*x^2))) \\ G. C. Greubel, Sep 24 2018
(MAGMA) [Numerator((&+[(-1)^k*Factorial(n)*(26/27)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Sep 24 2018
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| STATUS
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approved
editing
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#6 by Charles R Greathouse IV at Fri Jan 29 15:31:01 EST 2016
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#5 by Charles R Greathouse IV at Fri Jan 29 15:30:41 EST 2016
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#4 by R. J. Mathar at Mon Feb 24 15:55:58 EST 2014
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#3 by R. J. Mathar at Mon Feb 24 15:55:52 EST 2014
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| EXAMPLE
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Numerators of 1, 26/27, -782/729, -96148/19683, 920620/531441
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| CROSSREFS
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The denominators are an easily recognizable sequence.
Cf. A009971 (denominators).
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| STATUS
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approved
editing
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#2 by Russ Cox at Fri Mar 30 16:51:20 EDT 2012
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| AUTHOR
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_N. J. A. Sloane (njas(AT)research.att.com), _, Nov 12 2009
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Discussion
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| Fri Mar 30
| 16:51
| OEIS Server: https://oeis.org/edit/global/110
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