A303533 Number of ordered direct sum decompositions of the vector space GF(2)^n.

1, 1, 7, 225, 31041, 17698273, 41014759873, 383214694567809, 14378402336340492033, 2162169920997910948019713, 1301828396408136687071569640449, 3136821919822089791220365613645953025, 30240714417270288646830264781681630189187073

Offset: 0

Author

Geoffrey Critzer, Apr 25 2018

Keywords

• nonn

Crossrefs

Cf. A270881.

Programs

Mathematica

nn = 12; \[Gamma][n_] := (q - 1)^n  q^Binomial[n, 2] FunctionExpand[QFactorial[n, q]] /. q -> 2; \[CapitalGamma][z_] :=
Sum[z^k/\[Gamma][k], {k, 0, nn}];Table[\[Gamma][n], {n, 0, nn}] CoefficientList[Series[1/(1 - (\[CapitalGamma][z] - 1)), {z, 0, nn}], z]

Formula

Sum_{n>=0}a(n)x^n/g(n) = 1/(2-(Sum_{n>=0}x^n/g(n))) where g(n) = A002884(n).

a(n) ~ c * d^n * 2^(n^2), where d = 1.149524744759658194895953141071829185374022882216951573931... and c = 0.2546517972696293457891304601766804587838159436304512... - Vaclav Kotesovec, May 06 2018