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AC[d_Integer] := Module[{C, M, p}, (* from W. Y. C. Chen algorithm *) M[p_List] := Plus @@ p!/(Times @@ p * Times @@ (Length /@ Split[p]!)); C[p_List, q_List] := Module[{r, m, k, x}, r = If[0 == Length[q], 1, 2*2^IntegerExponent[LCM @@ q, 2]]; m = LCM @@ Join[p/GCD[r, p], q/GCD[r, q]]; CoefficientList[Expand[Product[(1 + x^(k *r))^((Plus @@ Map[MoebiusMu[k/#]*2^Plus @@ GCD[#*r, Join[p, q]]&, Divisors[k]])/(k*r)), {k, 1, m}]], x]]; Sum[Binomial[d, p]*Plus @@ Plus @@ Outer[M[#1] M[#2] C[#1, #2]*2^(d - Length[#1] - Length[#2]) &, P[p], P[d - p], 1], {p, 0, d}]/(d! 2^d)]; AC[0] = {1, 1};
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D. Condon, S. Coskey, L. Serafin, and C. Stockdale, <a href="http://arxiv.org/abs/1412.4683">On generalizations of separating and splitting families</a>, arXiv preprint arXiv:1412.4683 [math.CO], 2014-2015.
H. Harald Fripertinger, <a href="http://dx.doi.org/10.1023/A:1008248618779">Enumeration, construction and random generation of block codes</a>, Designs, Codes, Crypt., 14 (1998), 213-219.
H. Harald Fripertinger, <a href="http://www.mathe2.uni-bayreuth.de/frib/codes/tables.html">Isometry Classes of Codes</a>
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Add T(0, 1) = 1 inserted. (There are two 0-ary functions.) _- _Tilman Piesk_, Jan 10 2023
k 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 sums
0 1 1 2
1 1 1 1 3
2 1 1 2 1 1 6
3 1 1 3 3 6 3 3 1 1 22
4 1 1 4 6 19 27 50 56 74 56 50 27 19 6 4 1 1 402
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1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 3, 3, 6, 3, 3, 1, 1, 1, 1, 4, 6, 19, 27, 50, 56, 74, 56, 50, 27, 19, 6, 4, 1, 1, 1, 1, 5, 10, 47, 131, 472, 1326, 3779, 9013, 19963, 38073, 65664, 98804, 133576, 158658, 169112, 158658, 133576, 98804, 65664, 38073, 19963, 9013, 3779, 1326, 472, 131, 47, 10, 5, 1, 1
0,78
0 1 1 2
Add T(0, 1) = 1. (There are two 0-ary functions.) Tilman Piesk, Jan 10 2023
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