A220222 Triangular array read by rows. T(n,k) is the number of functional digraphs on {1,2,...,n} such that no node is at a distance greater than one from a cycle and there are k recurrent elements whose preimage contains only one element, n>=0, 0<=k<=n.

1, 0, 1, 2, 0, 2, 3, 12, 0, 6, 28, 24, 72, 0, 24, 125, 400, 180, 480, 0, 120, 1146, 2220, 4680, 1440, 3600, 0, 720, 8827, 29064, 30870, 53760, 12600, 30240, 0, 5040, 94200, 272272, 545328, 409920, 638400, 120960, 282240, 0, 40320, 1007001, 3722688, 5989032, 9386496, 5518800, 7983360, 1270080, 2903040, 0, 362880

Offset

0,4

Comments

Row sums = A006153. Column for k=0 is A052848.

Links

Table of n, a(n) for n=0..54.

Formula

E.g.f.: 1/(1 - x*(exp(x) -1 + y)).

Example

1,
0,    1,
2,    0,    2,
3,    12,   0,    6,
28,   24,   72,   0,    24,
125,  400,  180,  480,  0,    120, 0
1146, 2220, 4680, 1440, 3600, 0,   720

Mathematica

nn=6; a=x Exp[x]; Range[0, nn]!CoefficientList[Series[1/(1-x (Exp[x]-1+y)), {x, 0, nn}], {x, y}]//Grid

Crossrefs

Cf. A006153.

Sequence in context: A226432 A072514 A071547 * A089839 A206823 A335407

Adjacent sequences: A220219 A220220 A220221 * A220223 A220224 A220225

Keyword

nonn,tabl

Author

Geoffrey Critzer, Dec 07 2012

Status

approved