OFFSET
1,2
COMMENTS
Table with rows n=1,2,... and columns k=1,2,3,... is read along antidiagonals.
LINKS
David Callan, A determinant of Stirling Cycle Numbers Count Unlabeled Acyclic Single-Source Automata math.CO/0704.0004.
Manosij Ghosh Dastidar and Michael Wallner, Asymptotics of relaxed k-ary trees, arXiv:2404.08415 [math.CO], 2024. See p. 1.4.
MAPLE
T := proc(n, k) local kn, A, i, j ; kn := k*n ; A := matrix(kn, kn) ; for i from 1 to kn do for j from 1 to kn do A[i, j] := abs(combinat[stirling1](floor((i-1)/k)+2, floor((i-1)/k)+1+i-j)) ; od ; od ; linalg[det](A) ; end: for d from 1 to 9 do for n from d to 1 by -1 do k := d+1-n ; printf("%d, ", T(n, k)) ; od ; od;
MATHEMATICA
t[n_, k_] := Module[{kn, a, i, j}, kn = k*n; For[i = 1, i <= kn, i++, For[j = 1, j <= kn, j++, a[i, j] = Abs[StirlingS1[Floor[(i-1)/k]+2, Max[0, Floor[(i-1)/k]+1+i-j]]]]]; Det[Array[a, {kn, kn}]]]; Table[t[n-k, k], {n, 1, 10}, {k, 1, n-1}] // Flatten (* Jean-François Alcover, Jan 10 2014, translated from Maple *)
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
R. J. Mathar, May 09 2007
STATUS
approved