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A158903
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Numerator of Hermite(n, 2/3).
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1
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1, 4, -2, -152, -500, 8944, 80776, -642848, -12749168, 41573440, 2231658976, 1443416704, -436094810432, -2056157249792, 93821556641920, 893437853515264, -21758068879257344, -344342377329425408, 5280599567735045632, 132689328525674014720, -1275207738062689547264
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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) = 3^n * Hermite(n, 2/3).
E.g.f.: exp(4*x - 9*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(4/3)^(n-2*k)/(k!*(n-2*k)!)). (End)
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MATHEMATICA
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Table[3^n*HermiteH[n, 2/3], {n, 0, 30}] (* G. C. Greubel, Jul 13 2018 *)
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PROG
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(PARI) x='x+O('x^30); Vec(serlaplace(exp(4*x - 9*x^2))) \\ G. C. Greubel, Jul 13 2018
(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(4/3)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Jul 13 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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