A308476 - OEIS

%I #9 Mar 08 2021 22:26:41

%S 1,1,4,25,366,5491,176569,5332097,276268942,13470365431,1135683784753,

%T 75066413338423,9256260956838520,918768523598548169,

%U 140268128758724744770,18398287904991375995745,3879391299475140314514162,594721341754741064012714341

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

%H G. C. Greubel, <a href="/A308476/b308476.txt">Table of n, a(n) for n = 1..250</a>

%p a := proc(n) local j; option remember;

%p if n = 1 then 1;

%p else add(`if`(gcd(n, j) = 1, Stirling2(n, j)*a(j), 0), j = 1 .. n - 1);

%p end if; end proc;

%p seq(a(n), n = 1 .. 30); # _G. C. Greubel_, Mar 08 2021

%t 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 (Sage)

%o @CachedFunction

%o def a(n):

%o     if n==1: return 1

%o     else: return sum( stirling_number2(n,j)*a(j) if gcd(n,j)==1 else 0 for j in (1..n-1) )

%o [a(n) for n in (1..30)] # _G. C. Greubel_, Mar 08 2021

%Y Cf. A005121, A045545, A308463.

%K nonn

%O 1,3

%A _Ilya Gutkovskiy_, May 29 2019