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a(n) = Sum_{m=1..n} gcd(s(n,m), S(n,m)), where s(n,m) is an unsigned Stirling number of the first kind and S(n,m) is a Stirling number of the second kind.
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%I #9 Jan 22 2019 23:00:32

%S 1,2,5,9,22,68,163,136,525,14519,3918,5954,26561,23897,875479,464545,

%T 303146,1576515,15328385,1297494,25992621,92698823,64096034,31484634,

%U 16667307085,737157766,397339059223,115011291216,30816653208,4304179162

%N a(n) = Sum_{m=1..n} gcd(s(n,m), S(n,m)), where s(n,m) is an unsigned Stirling number of the first kind and S(n,m) is a Stirling number of the second kind.

%p with(combinat): T:=(n,k)->gcd(abs(stirling1(n,k)),stirling2(n,k)): seq(add(T(n,k),k=1..n),n=1..35); # _Emeric Deutsch_, Feb 25 2007

%K nonn

%O 1,2

%A _Leroy Quet_, Feb 22 2007

%E More terms from _Emeric Deutsch_, Feb 25 2007