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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. 0
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 (list; table; graph; refs; listen; history; text; internal format)
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

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Last modified December 1 22:12 EST 2021. Contains 349435 sequences. (Running on oeis4.)