A357925 a(n) = Sum_{k=0..floor(n/3)} Stirling2(n - 2*k,n - 3*k).
1, 1, 1, 1, 2, 4, 7, 12, 23, 47, 95, 192, 402, 869, 1898, 4181, 9379, 21431, 49556, 115770, 273919, 656476, 1590061, 3888783, 9608337, 23980678, 60402964, 153469477, 393325442, 1016628823, 2648842279, 6955029849, 18400676786, 49042936328, 131646082259
Offset: 0
Keywords
Programs
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Mathematica
Table[Sum[StirlingS2[n-2k,n-3k],{k,0,Floor[n/3]}],{n,0,40}] (* Harvey P. Dale, Feb 22 2024 *) -
PARI
a(n) = sum(k=0, n\3, stirling(n-2*k, n-3*k, 2));
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PARI
my(N=40, x='x+O('x^N)); Vec(sum(k=0, N, x^k/prod(j=1, k, 1-j*x^3)))
Formula
G.f.: Sum_{k>=0} x^k/Product_{j=1..k} (1 - j * x^3).