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A289543 Number of direct sum decompositions of GF(2)^n that do not contain any subspaces of dimension 1. 1
1, 0, 1, 1, 281, 9921, 16078337, 13596908545, 191426147495937, 3273234077014474753, 497324772153177747947521, 154709087482207635347155451905, 291534668371237082293312814285062145, 1534814232386517133354150755522868689240065, 39269743760371912650589750432327799926355436503041, 3338607968166762847572429548161284663670177988768356630529 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

q-analog of A000296.

LINKS

Table of n, a(n) for n=0..15.

David Ellerman, The number of direct-sum decompositions of a finite vector space, arXiv:1603.07619 [math.CO], 2016.

Kent E. Morrison, Integer Sequences and Matrices Over Finite Fields, Journal of Integer Sequences, Vol. 9 (2006), Article 06.2.1

FORMULA

a(n)/A002884(n) is the coefficient of x^n in the expansion of exp(Sum_{k>1}x^k/A002884(k)).

MATHEMATICA

nn = 15; q := 2; g[n_] := (q - 1)^n  q^Binomial[n, 2] FunctionExpand[QFactorial[n, q]]; G[z_] :=Sum[z^k/g[k], {k, 1, nn}]; Table[g[n], {n, 0, nn}] CoefficientList[

  Series[Exp[G[z] - z], {z, 0, nn}], z]

CROSSREFS

Cf. A270881, A287406.

Sequence in context: A108836 A295983 A264150 * A270964 A185710 A242982

Adjacent sequences:  A289540 A289541 A289542 * A289544 A289545 A289546

KEYWORD

nonn

AUTHOR

Geoffrey Critzer, Jul 19 2017

STATUS

approved

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Last modified March 8 07:37 EST 2021. Contains 341941 sequences. (Running on oeis4.)