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A307376
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a(n) = 1/n! * Sum_{k=0..n} (2*n+k)!/((n-k)!*k!*2^k).
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1
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1, 5, 81, 2330, 97405, 5360607, 366432990, 29948982492, 2849278444155, 309333396512855, 37741150862494651, 5112458462852223210, 761358344010536141506, 123636426598733578925150, 21742842987398075489784900, 4116720379411455407932693320, 834934865669512891440715729125
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OFFSET
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0,2
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LINKS
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FORMULA
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a(n) ~ 3^(3*n + 1/2) * n^(n - 1/2) / (sqrt(Pi) * 2^(n + 1/2) * exp(n - 2/3)). - Vaclav Kotesovec, Apr 06 2019
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MATHEMATICA
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Table[Sum[(2*n + k)!/((n - k)!*k!*2^k)/n!, {k, 0, n}], {n, 0, 20}] (* Vaclav Kotesovec, Apr 06 2019 *)
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PROG
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(PARI) {a(n) = sum(k=0, n, (2*n+k)!/((n-k)!*k!*2^k))/n!}
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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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