OFFSET
0,6
LINKS
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
Sum_{n>=0}T(n,k)*u^n/g(n)*t^k = exp(Sum_{r>=0}u^r/g(r) - 1 - u + t*u) where g(n) is A002884(n).
EXAMPLE
1,
0, 1,
1, 0, 3,
1, 28, 0, 28,
281, 120, 1680, 0, 840,
9921, 139376, 29760, 277760, 0, 83328,
MATHEMATICA
nn = 8; g[n_] := QFactorial[n, q]*(q - 1)^n*q^Binomial[n, 2] /. q -> 2; e[u_] := Sum[u^r/g[r], {r, 0, nn}];
Table[Table[(Table[g[n], {n, 0, nn}] CoefficientList[ Series[Exp[e[u] - 1 - u + u t], {u, 0, nn}], {u, t}])[[n,
k]], {k, 1, n}], {n, 1, nn + 1}] // Grid
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Geoffrey Critzer, May 21 2017
STATUS
approved