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A159649
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Numerator of Hermite(n, 11/19).
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1
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1, 22, -238, -37004, -298580, 100298792, 3284447224, -362236528016, -24568799886448, 1551764588318560, 193786882605147424, -6940428910346759872, -1691744857677709558592, 22913489210334717241984, 16382813996790345696268160, 128812358991324283435925248
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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) - 22*a(n-1) + 722*(n-1)*a(n-2) = 0. [DLMF] - R. J. Mathar, Feb 16 2014
a(n) = 19^n * Hermite(n, 11/19).
E.g.f.: exp(22*x - 361*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(22/19)^(n-2*k)/(k!*(n-2*k)!)). (End)
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EXAMPLE
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Numerator of 1, 22/19, -238/361, -37004/6859, -298580/130321, 100298792/2476099, ...
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MAPLE
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orthopoly[H](n, 11/19) ;
numer(%) ;
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MATHEMATICA
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Table[19^n*HermiteH[n, 11/19], {n, 0, 50}] (* G. C. Greubel, Jul 11 2018 *)
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PROG
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(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(22/19)^(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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