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A333984
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a(0) = 0; a(n) = 5^(n-1) + (1/n) * Sum_{k=1..n-1} binomial(n,k)^2 * 5^(k-1) * (n-k) * a(n-k).
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4
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0, 1, 7, 82, 1839, 69630, 3950650, 313747050, 33224570175, 4523562983350, 769859662962750, 160137417877796250, 39971947204607486250, 11791483690935887486250, 4058152793413483423916250, 1611522009185095020022068750, 731368135285580087866788609375, 376178084508304435598172207843750
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OFFSET
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0,3
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LINKS
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Table of n, a(n) for n=0..17.
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FORMULA
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Sum_{n>=0} a(n) * x^n / (n!)^2 = -log((6 - BesselI(0,2*sqrt(5*x))) / 5).
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MATHEMATICA
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a[0] = 0; a[n_] := a[n] = 5^(n - 1) + (1/n) Sum[Binomial[n, k]^2 5^(k - 1) (n - k) a[n - k], {k, 1, n - 1}]; Table[a[n], {n, 0, 17}]
nmax = 17; CoefficientList[Series[-Log[(6 - BesselI[0, 2 Sqrt[5 x]])/5], {x, 0, nmax}], x] Range[0, nmax]!^2
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CROSSREFS
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Cf. A102223, A333981, A333982, A333983, A333985, A337595.
Sequence in context: A243672 A268653 A242375 * A244821 A304591 A139951
Adjacent sequences: A333981 A333982 A333983 * A333985 A333986 A333987
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KEYWORD
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nonn
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AUTHOR
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Ilya Gutkovskiy, Sep 04 2020
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STATUS
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approved
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