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A159622
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Numerator of Hermite(n, 5/19).
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1
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1, 10, -622, -20660, 1140652, 71072600, -3407027720, -341956780400, 13799550292880, 2113137866519200, -68538099137942240, -15942236387648046400, 384907219477056806080, 141972608257353242070400, -2193013079438122761162880, -1456989255059707798459232000
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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) = 19^n * Hermite(n, 5/19).
E.g.f.: exp(10*x - 361*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(10/19)^(n-2*k)/(k!*(n-2*k)!)). (End)
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MATHEMATICA
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Table[19^n*HermiteH[n, 5/19], {n, 0, 30}] (* G. C. Greubel, Jul 14 2018 *)
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PROG
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(PARI) x='x+O('x^30); Vec(serlaplace(exp(10*x - 361*x^2))) \\ G. C. Greubel, Jul 14 2018
(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(10/19)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Jul 14 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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