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a(n) = Sum_{k=0..floor(n/4)} Stirling2(k,n - 4*k).
2

%I #11 Oct 22 2022 14:01:51

%S 1,0,0,0,0,1,0,0,0,1,1,0,0,1,3,1,0,1,7,6,1,1,15,25,10,2,31,90,65,16,

%T 64,301,350,141,148,967,1701,1051,521,3053,7771,6952,3157,9792,34141,

%U 42527,23850,34381,146500,246776,181535,150513,623381,1380556,1327802,889022,2691557,7530777

%N a(n) = Sum_{k=0..floor(n/4)} Stirling2(k,n - 4*k).

%F G.f.: Sum_{k>=0} x^(5*k)/Product_{j=1..k} (1 - j * x^4).

%o (PARI) a(n) = sum(k=0, n\4, stirling(k, n-4*k, 2));

%o (PARI) my(N=60, x='x+O('x^N)); Vec(sum(k=0, N, x^(5*k)/prod(j=1, k, 1-j*x^4)))

%Y Cf. A357939, A357940.

%Y Cf. A357926.

%K nonn

%O 0,15

%A _Seiichi Manyama_, Oct 21 2022