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A159883
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Numerator of Hermite(n, 14/23).
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1
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1, 28, -274, -66920, -1004084, 255091088, 12454154824, -1270601891552, -127812323590000, 7175629349576128, 1417946567012111584, -36215654642176309888, -17516100476867891291456, -30656862015230525822720, 240058053822414522099649664, 7175714947197201167276319232
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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) = 23^n * Hermite(n, 14/23).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(28/23)^(n-2*k)/(k!*(n-2*k)!)). (End)
D-finite with recurrence a(n) -28*a(n-1) +1058*(n-1)*a(n-2)=0. [DLMF] - R. J. Mathar, Feb 06 2021
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EXAMPLE
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Numerators of 1, 28/23, -274/529, -66920/12167, -1004084/279841, ...
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MATHEMATICA
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Numerator[Table[HermiteH[n, 14/23], {n, 0, 40}]] (* Vincenzo Librandi, Jun 23 2018 *)
Table[23^n*HermiteH[n, 14/23], {n, 0, 30}] (* G. C. Greubel, Jul 11 2018 *)
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PROG
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(PARI) x='x+O('x^99); Vec(serlaplace(exp(-529*x^2+28*x))) \\ Altug Alkan, Jul 30 2018
(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(28/23)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..20]]; // Vincenzo Librandi, Jun 23 2018
(GAP) List(List([0..20], n->Sum([0..Int(n/2)], k->(-1)^k*Factorial(n)*(28/23)^(n-2*k)/(Factorial(k)*Factorial(n-2*k)))), NumeratorRat); # Muniru A Asiru, Jul 12 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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