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A308476
a(1) = 1; a(n) = Sum_{k=1..n-1, gcd(n,k) = 1} Stirling2(n,k)*a(k).
1
1, 1, 4, 25, 366, 5491, 176569, 5332097, 276268942, 13470365431, 1135683784753, 75066413338423, 9256260956838520, 918768523598548169, 140268128758724744770, 18398287904991375995745, 3879391299475140314514162, 594721341754741064012714341
OFFSET
1,3
LINKS
MAPLE
a := proc(n) local j; option remember;
if n = 1 then 1;
else add(`if`(gcd(n, j) = 1, Stirling2(n, j)*a(j), 0), j = 1 .. n - 1);
end if; end proc;
seq(a(n), n = 1 .. 30); # G. C. Greubel, Mar 08 2021
MATHEMATICA
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}]
PROG
(Sage)
@CachedFunction
def a(n):
if n==1: return 1
else: return sum( stirling_number2(n, j)*a(j) if gcd(n, j)==1 else 0 for j in (1..n-1) )
[a(n) for n in (1..30)] # G. C. Greubel, Mar 08 2021
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, May 29 2019
STATUS
approved