cp's OEIS Frontend

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.

%I A373536 #8 Jun 28 2024 22:57:15
%S A373536 1,1,9,364,61320,41747328,113420740608,1223445790457856,
%T A373536 52307167449899335680,8861896666997422628536320,
%U A373536 5951934931285476447488997064704,15857359709817958217841735837828513792,167702614892018104786663957623269078052372480,7044769706183185876455816992603242619680927682396160
%N 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.
%H A373536 David Ellerman, <a href="http://arxiv.org/abs/1603.07619">The number of direct-sum decompositions of a finite vector space</a>, arXiv:1603.07619 [math.CO], 2016.
%H A373536 R. P. Stanley, <a href="http://www-math.mit.edu/~rstan/pubs/pubfiles/37.pdf">Exponential structures</a>
%F A373536 a(n) = A000262(n)*A053601(n).
%F A373536 Sum_{n>=0} a(n)*x^n/A002884(n) = exp(x/(1-x)).
%t A373536 nn = 13; B[n_] := Product[q^n - q^i, {i, 0, n - 1}] /. q -> 2;
%t A373536 e[x_] := Sum[x^n/B[n], {n, 0, nn}]; f[x_] := Sum[x^n, {n, 0, nn}];
%t A373536 Table[B[n], {n, 0, nn}] CoefficientList[Series[Exp[f[x] - 1], {x, 0, nn}], x]
%Y A373536 Cf. A270880, A000262, A053601, A002884.
%K A373536 nonn
%O A373536 0,3
%A A373536 _Geoffrey Critzer_, Jun 08 2024