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

1, 1, 4, 25, 366, 5491, 176569, 5332097, 276268942, 13470365431, 1135683784753, 75066413338423, 9256260956838520, 918768523598548169, 140268128758724744770, 18398287904991375995745, 3879391299475140314514162, 594721341754741064012714341

Offset: 1

Author

Ilya Gutkovskiy, May 29 2019

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 1..250

Crossrefs

Cf. A005121, A045545, A308463.

Programs

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}]

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