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A159946
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Numerator of Hermite(n, 20/23).
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1
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1, 40, 542, -62960, -4238708, 96898400, 26298701320, 436837009600, -177294701591920, -10789176512931200, 1256633088041014240, 164414811028452665600, -8048103437483217101120, -2409334578316563726502400, 14320231546481618948708480, 36259873035884206674901888000
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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..385
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FORMULA
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From G. C. Greubel, Jul 16 2018: (Start)
a(n) = 23^n * Hermite(n, 20/23).
E.g.f.: exp(40*x - 529*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(40/23)^(n-2*k)/(k!*(n-2*k)!)). (End)
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EXAMPLE
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Numerators of 1, 40/23, 542/529, -62960/12167, -4238708/279841, ...
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MATHEMATICA
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Numerator[Table[HermiteH[n, 20/23], {n, 0, 30}]] (* or *) Table[23^n * HermiteH[n, 20/23], {n, 0, 30}] (* G. C. Greubel, Jul 16 2018 *)
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PROG
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(PARI) a(n)=numerator(polhermite(n, 20/23)) \\ Charles R Greathouse IV, Jan 29 2016
(PARI) x='x+O('x^30); Vec(serlaplace(exp(40*x - 529*x^2))) \\ G. C. Greubel, Jul 16 2018
(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(40/23)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Jul 16 2018
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CROSSREFS
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Cf. A009967 (denominators).
Sequence in context: A269692 A247409 A107419 * A185744 A269497 A097823
Adjacent sequences: A159943 A159944 A159945 * A159947 A159948 A159949
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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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