A308475 - OEIS

%I #9 Mar 08 2021 20:07:41

%S 1,2,9,40,315,1896,21651,191360,2546487,28064080,488517183,5879603280,

%T 124673371719,1928346159572,42684093159480,754925802649360,

%U 20289814995554811,366300418631427144,11352374441063693655,250187625076714423520,7774760839170720287739

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

%H G. C. Greubel, <a href="/A308475/b308475.txt">Table of n, a(n) for n = 1..425</a>

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

%p if n=1 then 1;

%p else add( `if`(gcd(n,j)=1, binomial(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, Binomial[n, k] a[k], 0], {k, 1, n - 1}]; a[1] = 1; Table[a[n], {n, 1, 21}]

%o (Sage)

%o @CachedFunction

%o def a(n):

%o     if n==1: return 1

%o     else: return sum( kronecker_delta(gcd(n,j), 1)*binomial(n,j)*a(j) for j in (1..n-1) )

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

%Y Cf. A000670, A045545, A052882, A056188.

%K nonn

%O 1,2

%A _Ilya Gutkovskiy_, May 29 2019