A308475 a(1) = 1; a(n) = Sum_{k=1..n-1, gcd(n,k) = 1} binomial(n,k)*a(k).

1, 2, 9, 40, 315, 1896, 21651, 191360, 2546487, 28064080, 488517183, 5879603280, 124673371719, 1928346159572, 42684093159480, 754925802649360, 20289814995554811, 366300418631427144, 11352374441063693655, 250187625076714423520, 7774760839170720287739

Offset: 1

Author

Ilya Gutkovskiy, May 29 2019

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 1..425

Crossrefs

Cf. A000670, A045545, A052882, A056188.

Programs

Maple

a:= proc(n) option remember;
if n=1 then 1;
else add( `if`(gcd(n,j)=1, binomial(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, Binomial[n, k] a[k], 0], {k, 1, n - 1}]; a[1] = 1; Table[a[n], {n, 1, 21}]

Sage

@CachedFunction
def a(n):
    if n==1: return 1
    else: return sum( kronecker_delta(gcd(n,j), 1)*binomial(n,j)*a(j) for j in (1..n-1) )
[a(n) for n in (1..30)] # G. C. Greubel, Mar 08 2021