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A159655
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Numerator of Hermite(n, 17/19).
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1
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1, 34, 434, -34340, -2107604, 27515384, 8543973496, 171298455376, -37357094566000, -2259561093495776, 165921323311011616, 21955356087613897664, -571265042757181733696, -209644216596830988306560, -1766009672973345849952384, 2059039412479673870904327424
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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) -34*a(n-1) +722*(n-1)*a(n-2)=0. [DLMF] - R. J. Mathar, Feb 16 2014
a(n) = 19^n * Hermite(n, 17/19).
E.g.f.: exp(34*x - 361*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(34/19)^(n-2*k)/(k!*(n-2*k)!)). (End)
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EXAMPLE
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Numerator of 1, 34/19, 434/361, -34340/6859, -2107604/130321, 27515384/2476099,..
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MAPLE
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orthopoly[H](n, 17/19) ;
numer(%) ;
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MATHEMATICA
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Table[19^n*HermiteH[n, 17/19], {n, 0, 50}] (* G. C. Greubel, Jul 11 2018 *)
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PROG
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(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(34/19)^(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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