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a(n) = floor(Sum_{m=1..n} Stirling2(n,m) / binomial(n-1,m-1)).
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%I #15 Jan 10 2024 04:58:12

%S 1,2,3,6,12,26,62,161,448,1338,4274,14524,52289,198678,794065,3328482,

%T 14594217,66779091,318205958,1575994324,8098891289,43115440260,

%U 237435483669,1350777074576,7928871324300,47965914249016,298735745451523

%N a(n) = floor(Sum_{m=1..n} Stirling2(n,m) / binomial(n-1,m-1)).

%o (SageMath)

%o print([int(sum(stirling_number2(n, m)/binomial(n-1, m-1) for m in [1..n])) for n in [1..27]]) # _Andrey Zabolotskiy_, Jan 09 2024

%Y Cf. A024423, A024424, A024425.

%K nonn

%O 1,2

%A _Clark Kimberling_