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A160063
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Numerator of Hermite(n, 18/25).
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1
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1, 36, 46, -88344, -3352884, 321016176, 32512107336, -1237185455904, -329019615602544, 527148397348416, 3720448017833162976, 127346773675138667136, -46571676392900998903104, -3586781955271515967551744, 627665590994866657343577216, 85364645493066729096524299776
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OFFSET
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0,2
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LINKS
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FORMULA
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a(n) = 25^n * Hermite(n, 18/25).
E.g.f.: exp(36*x - 625*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(36/25)^(n-2*k)/(k!*(n-2*k)!)). (End)
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EXAMPLE
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Numerators of 1, 36/25, 46/625, -88344/15625, -3352884/390625, ...
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MATHEMATICA
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Numerator[HermiteH[Range[0, 20], 18/25]] (* Harvey P. Dale, Mar 18 2015 *)
Table[25^n*HermiteH[n, 18/25], {n, 0, 30}] (* G. C. Greubel, Sep 23 2018 *)
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PROG
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(PARI) x='x+O('x^30); Vec(serlaplace(exp(36*x - 625*x^2))) \\ G. C. Greubel, Sep 23 2018
(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(36/25)^(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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KEYWORD
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sign,frac
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AUTHOR
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STATUS
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approved
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