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A160010
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Numerator of Hermite(n, 6/25).
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1
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1, 12, -1106, -43272, 3628236, 259898832, -19557689016, -2183933508192, 144922576791696, 23578406003420352, -1347438116865535776, -310899332445140829312, 14796482117559426968256, 4841047772087825563299072, -182350261145286781474571136, -86906539145280388735428613632
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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, 6/25).
E.g.f.: exp(12*x - 625*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(12/25)^(n-2*k)/(k!*(n-2*k)!)). (End)
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EXAMPLE
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Numerators of 1, 12/25, -1106/625, -43272/15625, 3628236/390625
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MAPLE
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seq(coeff(series(factorial(n)*exp(12*x-625*x^2), x, n+1), x, n), n=0..15); # Muniru A Asiru, Jul 17 2018
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MATHEMATICA
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Numerator[Table[HermiteH[n, 6/25], {n, 0, 30}]] (* or *) Table[25^n* HermiteH[n, 6/25], {n, 0, 30}] (* G. C. Greubel, Jul 17 2018 *)
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PROG
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(PARI) x='x+O('x^30); Vec(serlaplace(exp(12*x - 625*x^2))) \\ G. C. Greubel, Jul 17 2018
(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(12/25)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Jul 17 2018
(GAP) List(List([0..15], n->Sum([0..Int(n/2)], k->(-1)^k*Factorial(n)*(12/25)^(n-2*k)/(Factorial(k)*Factorial(n-2*k)))), NumeratorRat); # Muniru A Asiru, Jul 17 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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