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A372829
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a(n) = n! * Sum_{k=0..floor(n/2)} k! / (2*k)!.
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0
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1, 1, 3, 9, 38, 190, 1146, 8022, 64200, 577800, 5778120, 63559320, 762712560, 9915263280, 138813690960, 2082205364400, 33315285870720, 566359859802240, 10194477476803200, 193695072059260800, 3873901441188844800, 81351930264965740800, 1789742465829286214400
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OFFSET
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0,3
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LINKS
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FORMULA
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E.g.f.: (1 + sqrt(Pi) * x * exp(x^2/4) * erf(x/2) / 2) / (1 - x).
a(n) = Sum_{k=0..floor(n/2)} binomial(n,2*k) * k! * (n-2*k)!.
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MATHEMATICA
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Table[n! Sum[k!/(2 k)!, {k, 0, Floor[n/2]}], {n, 0, 22}]
nmax = 22; CoefficientList[Series[(1 + Sqrt[Pi] x Exp[x^2/4] Erf[x/2]/2)/(1 - x), {x, 0, nmax}], x] Range[0, nmax]!
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PROG
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(PARI) a(n) = n! * sum(k=0, n\2, k! / (2*k)!); \\ Michel Marcus, May 14 2024
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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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