OFFSET
0,3
LINKS
Kent E. Morrison, Integer Sequences and Matrices Over Finite Fields, Journal of Integer Sequences, Vol. 9 (2006), Article 06.2.1.
EXAMPLE
1;
0, 3;
18, 24, 39;
3456, 8190, 5928, 2109;
7619508, 17094240, 13700700, 4215120, 417153;
149200289280, 335730157884, 267485755680, 85615372260, 8910314160, 346720179;
MATHEMATICA
nn = 7; q = 3; b[p_, i_] := Count[p, i]; d[p_, i_] :=Sum[j b[p, j], {j, 1, i}] + i Sum[b[p, j], {j, i + 1, Total[p]}]; aut[deg_, p_] := Product[Product[q^(d[p, i] deg) - q^((d[p, i] - k) deg), {k, 1, b[p, i]}], {i, 1, Total[p]}]; A001037 =
Table[1/n Sum[MoebiusMu[n/d] q^d, {d, Divisors[n]}], {n, 1, nn}]; g[u_, v_] :=
Total[Map[v^Length[#] u^Total[#]/aut[1, #] &, Level[Table[IntegerPartitions[n], {n, 0, nn}], {2}]]]; Table[Take[(Table[ Product[q^n - q^i, {i, 0, n - 1}], {n, 0, nn}] CoefficientList[Series[g[u, v]^3 Product[Product[1/(1 - (u/q^r)^d), {r, 1, \[Infinity]}]^A001037[[d]], {d, 2, nn}], {u, 0, nn}], {u, v}])[[n]], n], {n, 1, nn}] // Grid
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Geoffrey Critzer, Jul 16 2021
STATUS
approved