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A228080
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(5*n+2)!/(2*(n!)^5), n >= 0.
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0
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1, 2520, 7484400, 22870848000, 70579794285000, 218799620836917120, 679953587124305894400, 2116187746296592370688000, 6592431144164903462359935000, 20550499897066845200729434200000, 64091912654977017603465324370118400, 199956261330234671205699024876891648000
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OFFSET
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0,2
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COMMENTS
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Although limit( a(n)^(1/n), n=infinity ) = 5^5, apparently this sequence is not a Hausdorff moment sequence of any positive function on (0,5^5).
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LINKS
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FORMULA
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In Maple notation:
O.g.f. : hypergeom([3/5, 4/5, 6/5, 7/5], [1, 1, 1], 5^5*z);
E.g.f. : hypergeom([3/5, 4/5, 6/5, 7/5], [1, 1, 1, 1], 5^5*z);
Asymptotics: a(n) -> (25*n^2+5*n-2)*(5^(5*n+1/2))* n^(-2)/(8*Pi^2), for n -> infinity.
D-finite with recurrence (n^4)*a(n) -5*(5*n+1)*(5*n+2)*(5*n-2)*(5*n-1)*a(n-1)=0. - R. J. Mathar, Jul 27 2022
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MAPLE
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seq((5*n+2)!/(2*(n!)^5), n=0..11).
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MATHEMATICA
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Table[(5n+2)!/(2(n!)^5), {n, 0, 15}] (* Harvey P. Dale, Aug 04 2019 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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