A357903 a(n) = Sum_{k=0..floor(n/3)} Stirling2(n - 2*k,k).
1, 0, 0, 1, 1, 1, 2, 4, 8, 17, 38, 89, 219, 567, 1543, 4400, 13094, 40507, 129874, 430731, 1476030, 5222544, 19066758, 71764369, 278166767, 1108986222, 4541765652, 19085377108, 82211094414, 362717859475, 1638071537802, 7567876937002, 35748311794246, 172558399424154
Offset: 0
Keywords
Programs
-
PARI
a(n) = sum(k=0, n\3, stirling(n-2*k, k, 2));
-
PARI
my(N=40, x='x+O('x^N)); Vec(sum(k=0, N, x^(3*k)/prod(j=1, k, 1-j*x)))
Formula
G.f.: Sum_{k>=0} x^(3*k)/Product_{j=1..k} (1 - j * x).