login
a(n) = Sum_{k=0..floor(n/3)} Stirling2(n - 2*k,k).
3

%I #9 Oct 19 2022 13:40:31

%S 1,0,0,1,1,1,2,4,8,17,38,89,219,567,1543,4400,13094,40507,129874,

%T 430731,1476030,5222544,19066758,71764369,278166767,1108986222,

%U 4541765652,19085377108,82211094414,362717859475,1638071537802,7567876937002,35748311794246,172558399424154

%N a(n) = Sum_{k=0..floor(n/3)} Stirling2(n - 2*k,k).

%F G.f.: Sum_{k>=0} x^(3*k)/Product_{j=1..k} (1 - j * x).

%o (PARI) a(n) = sum(k=0, n\3, stirling(n-2*k, k, 2));

%o (PARI) my(N=40, x='x+O('x^N)); Vec(sum(k=0, N, x^(3*k)/prod(j=1, k, 1-j*x)))

%Y Cf. A000110, A171367, A357904.

%K nonn

%O 0,7

%A _Seiichi Manyama_, Oct 19 2022