A287406 - OEIS

%I #6 May 27 2017 07:49:12

%S 1,1,1,29,121,10417,20167393,1405696961,1671421144961,

%T 34853495567335169,18070618208072153366017,76880583838185587571686401,

%U 5835812465544660559691588302849,6474896789559157455730381208091095041,143196455096491413680184647037773197755801601,76671942287512076984565827384061983641627409659183105

%N Number of direct sum decompositions of a finite vector space of n dimensions over GF(2) whose subspaces are all of distinct dimensions.

%C q analog of A007837.

%H  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 Kent E. Morrison, <a href="http://www.cs.uwaterloo.ca/journals/JIS/VOL9/Morrison/morrison37.html">Integer Sequences and Matrices Over Finite Fields</a>, Journal of Integer Sequences, Vol. 9 (2006), Article 06.2.1

%F Sum_{n>=0}a(n)u^n/g(n) = Product_{r>=1}1 + u^r/g(r) where g(n) = A002884(n).

%t nn = 15; g[n_] := QFactorial[n, q]*(q - 1)^n*q^Binomial[n, 2] /. q -> 2;

%t Table[g[n], {n, 0, nn}] CoefficientList[Series[Product[1 + u^r/g[r], {r, 1, nn}], {u, 0, nn}], u]

%K nonn

%O 0,4

%A _Geoffrey Critzer_, May 24 2017