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A128249 T(n,k) is the number of unlabeled acyclic single-source automata with n transient states on a (k+1)-letter input alphabet. 0
1, 3, 1, 16, 7, 1, 127, 139, 15, 1, 1363, 5711, 1000, 31, 1, 18628, 408354, 189035, 6631, 63, 1, 311250, 45605881, 79278446, 5470431, 42196, 127, 1, 6173791, 7390305396, 63263422646, 12703473581, 147606627, 262459, 255, 1, 142190703, 1647470410551 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Table with rows n=1,2,... and columns k=1,2,3,... is read along antidiagonals.

LINKS

Table of n, a(n) for n=1..38.

D. Callan, A determinant of Stirling Cycle Numbers Count Unlabeled Acyclic Single-Source Automata math.CO/0704.0004.

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

Cf. A082162, A082161.

Sequence in context: A143565 A143018 A102012 * A071211 A222029 A038675

Adjacent sequences:  A128246 A128247 A128248 * A128250 A128251 A128252

KEYWORD

nonn,tabl

AUTHOR

R. J. Mathar, May 09 2007

STATUS

approved

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Last modified February 15 22:28 EST 2019. Contains 320138 sequences. (Running on oeis4.)