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A159654
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Numerator of Hermite(n, 16/19).
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1
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1, 32, 302, -36544, -1823540, 47185792, 8092924744, 54564740864, -39155569948528, -1568144181583360, 204252279714867424, 17858073941907616768, -1050713239354433344832, -188345176292029458712576, 3834948823235768695790720, 2026511404303378366932021248
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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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D-finite with recurrence a(n) - 32*a(n-1) + 722*(n-1)*a(n-2) = 0. [DLMF] - R. J. Mathar, Feb 16 2014
a(n) = 19^n * Hermite(n, 16/19).
E.g.f.: exp(32*x - 361*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(32/19)^(n-2*k)/(k!*(n-2*k)!)). (End)
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EXAMPLE
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Numerator of 1, 32/19, 302/361, -36544/6859, -1823540/130321, 47185792/2476099, ...
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MAPLE
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orthopoly[H](n, 16/19) ;
numer(%) ;
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MATHEMATICA
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Table[19^n*HermiteH[n, 16/19], {n, 0, 50}] (* G. C. Greubel, Jul 11 2018 *)
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PROG
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(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(32/19)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Jul 11 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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