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A373536
Number of ways to form a direct sum decomposition of the vector space GF(2)^n and then choose a basis for each subspace in the decomposition.
0
1, 1, 9, 364, 61320, 41747328, 113420740608, 1223445790457856, 52307167449899335680, 8861896666997422628536320, 5951934931285476447488997064704, 15857359709817958217841735837828513792, 167702614892018104786663957623269078052372480, 7044769706183185876455816992603242619680927682396160
OFFSET
0,3
FORMULA
a(n) = A000262(n)*A053601(n).
Sum_{n>=0} a(n)*x^n/A002884(n) = exp(x/(1-x)).
MATHEMATICA
nn = 13; B[n_] := Product[q^n - q^i, {i, 0, n - 1}] /. q -> 2;
e[x_] := Sum[x^n/B[n], {n, 0, nn}]; f[x_] := Sum[x^n, {n, 0, nn}];
Table[B[n], {n, 0, nn}] CoefficientList[Series[Exp[f[x] - 1], {x, 0, nn}], x]
CROSSREFS
KEYWORD
nonn
AUTHOR
Geoffrey Critzer, Jun 08 2024
STATUS
approved