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A160066
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Numerator of Hermite(n, 22/25).
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1
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1, 44, 686, -79816, -6084404, 131366224, 43807638856, 942289429664, -341856105084784, -24464562920370496, 2769440413707518176, 427662414707761999744, -19262659441336846931264, -7262493236035251261135616, -6531486463827292856927104, 126806246226208496184168487424
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OFFSET
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0,2
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LINKS
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G. C. Greubel, Table of n, a(n) for n = 0..380
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FORMULA
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From G. C. Greubel, Sep 23 2018: (Start)
a(n) = 25^n * Hermite(n, 22/25).
E.g.f.: exp(44*x - 625*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(44/25)^(n-2*k)/(k!*(n-2*k)!)). (End)
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EXAMPLE
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Numerators of 1, 44/25, 686/625, -79816/15625, -6084404/390625, ...
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MATHEMATICA
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Table[25^n*HermiteH[n, 22/25], {n, 0, 30}] (* G. C. Greubel, Sep 23 2018 *)
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PROG
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(PARI) a(n)=numerator(polhermite(n, 22/25)) \\ Charles R Greathouse IV, Jan 29 2016
(PARI) x='x+O('x^30); Vec(serlaplace(exp(44*x - 625*x^2))) \\ G. C. Greubel, Sep 23 2018
(MAGMA) [Numerator((&+[(-1)^k*Factorial(n)*(44/25)^(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
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CROSSREFS
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Cf. A009969 (denominators).
Sequence in context: A252869 A296649 A221505 * A120812 A282860 A232139
Adjacent sequences: A160063 A160064 A160065 * A160067 A160068 A160069
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KEYWORD
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sign,frac
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AUTHOR
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N. J. A. Sloane, Nov 12 2009
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STATUS
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approved
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