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A185248
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Expansion of 3F2( (1/2, 3/2, 5/2); (3, 5))(64 x)
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2
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1, 8, 140, 3360, 97020, 3171168, 113369256, 4338459840, 175165316040, 7385525026880, 322747443674656, 14534919841012480, 671591162296782000, 31725844951938480000, 1527939354203180010000, 74847268228930016688000, 3722092276301165621547000
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OFFSET
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0,2
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COMMENTS
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Generalization of formula for A172392.
Combinatorial interpretation welcome.
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LINKS
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FORMULA
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D-finite with recurrence +n*(n+4)*(n+2)*a(n) -8*(2*n+3)*(2*n+1)*(2*n-1)*a(n-1)=0. - R. J. Mathar, Jul 27 2022
a(n) = 16 * (2*n+3) * (2*n+1)^2 * (2*n)!^3 / (n!^4 * (n+2)! * (n+4)!).
a(n) ~ 2^(6*n + 7) / (Pi^(3/2) * n^(9/2)). (End)
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MATHEMATICA
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CoefficientList[Series[HypergeometricPFQ[{1/2, 3/2, 5/2}, {3, 5}, 64 x], {x, 0, 20}], x]
Table[16 * (2*n+3) * (2*n+1)^2 * (2*n)!^3 / (n!^4 * (n+2)! * (n+4)!), {n, 0, 20}] (* Vaclav Kotesovec, Feb 17 2024 *)
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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