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A308476 a(1) = 1; a(n) = Sum_{k=1..n-1, gcd(n,k) = 1} Stirling2(n,k)*a(k).

%I A308476 #9 Mar 08 2021 22:26:41
%S A308476 1,1,4,25,366,5491,176569,5332097,276268942,13470365431,1135683784753,
%T A308476 75066413338423,9256260956838520,918768523598548169,
%U A308476 140268128758724744770,18398287904991375995745,3879391299475140314514162,594721341754741064012714341
%N A308476 a(1) = 1; a(n) = Sum_{k=1..n-1, gcd(n,k) = 1} Stirling2(n,k)*a(k).
%H A308476 G. C. Greubel, <a href="/A308476/b308476.txt">Table of n, a(n) for n = 1..250</a>
%p A308476 a := proc(n) local j; option remember;
%p A308476 if n = 1 then 1;
%p A308476 else add(`if`(gcd(n, j) = 1, Stirling2(n, j)*a(j), 0), j = 1 .. n - 1);
%p A308476 end if; end proc;
%p A308476 seq(a(n), n = 1 .. 30); # _G. C. Greubel_, Mar 08 2021
%t A308476 a[n_] := Sum[If[GCD[n, k] == 1, StirlingS2[n, k] a[k], 0], {k, 1, n - 1}]; a[1] = 1; Table[a[n], {n, 1, 18}]
%o A308476 (Sage)
%o A308476 @CachedFunction
%o A308476 def a(n):
%o A308476     if n==1: return 1
%o A308476     else: return sum( stirling_number2(n,j)*a(j) if gcd(n,j)==1 else 0 for j in (1..n-1) )
%o A308476 [a(n) for n in (1..30)] # _G. C. Greubel_, Mar 08 2021
%Y A308476 Cf. A005121, A045545, A308463.
%K A308476 nonn
%O A308476 1,3
%A A308476 _Ilya Gutkovskiy_, May 29 2019