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A295612
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a(n) = Sum_{k=0..n} binomial(n+k,k)^k.
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2
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1, 3, 40, 8105, 24053106, 1016507243472, 622366942086680904, 5608321882919220905812521, 752711651805019773658037206391596, 1518219710649896586598445898967340890577318, 46343146356260529633020448755386347142785083052620084
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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) = Sum_{k=0..n} A046899(n,k)^k.
a(n) ~ 2^(2*n^2) / (exp(1/8) * Pi^(n/2) * n^(n/2)). - Vaclav Kotesovec, Nov 25 2017
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MATHEMATICA
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Table[Sum[Binomial[n + k, k]^k, {k, 0, n}], {n, 0, 10}]
Table[Sum[((n + k)!/(n! k!))^k, {k, 0, n}], {n, 0, 10}]
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PROG
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(PARI) a(n) = sum(k=0, n, binomial(n+k, k)^k); \\ Michel Marcus, Nov 25 2017
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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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