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A305577
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a(n) = Sum_{k=0..n} k!!*(n - k)!!.
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2
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1, 2, 5, 10, 26, 58, 167, 414, 1324, 3606, 12729, 37674, 145578, 463770, 1944879, 6614190, 29852856, 107616150, 518782545, 1970493210, 10077228270, 40125873690, 216425656215, 899557170750, 5091758227620, 22011865939350, 130202223160905, 583641857191050, 3594820517111250
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OFFSET
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0,2
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COMMENTS
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Convolution of A006882 with itself.
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LINKS
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FORMULA
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G.f.: (Sum_{k>=0} k!!*x^k)^2.
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MAPLE
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a:= proc(n) option remember; `if`(n<4, n^2+1,
((3*n^2-4*n-2)*a(n-2) +(n+1)*a(n-3)
-2*a(n-1) -(n-1)^2*n*a(n-4))/(2*n-4))
end:
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MATHEMATICA
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Table[Sum[k!! (n - k)!!, {k, 0, n}], {n, 0, 28}]
nmax = 28; CoefficientList[Series[Sum[k!! x^k, {k, 0, nmax}]^2, {x, 0, nmax}], x]
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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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