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A203092 Triangular array read by rows.  T(n,k) is the number of partial functions on {1,2,...,n} that are endofunctions with no cycles of length > 1 that have exactly k components. 1
1, 1, 1, 1, 4, 1, 1, 18, 9, 1, 1, 116, 78, 16, 1, 1, 1060, 810, 220, 25, 1, 1, 12702, 10335, 3260, 495, 36, 1, 1, 187810, 158613, 54740, 9835, 966, 49, 1, 1, 3296120, 2854908, 1046024, 209510, 24696, 1708, 64, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

Row sums = A088957.

T(n,0)= 1,  the empty function.

T(n,n)= 1,  the identity function.

T(n,n-1)= n^2  (apparently).

LINKS

Table of n, a(n) for n=0..44.

FORMULA

E.g.f.: exp(x)*exp(y T(x)) where T(x) is the e.g.f. for A000169.

EXAMPLE

T(2,1)= 4 because there are 4 such partial functions on {1,2}: 1->1, 2->2, 1->1 2->1, 1->2 2->2,

1

1     1

1     4     1

1     18    9     1

1     116   78    16    1

1     1060  810   220   25    1

1     12702 10335 3260  495   36    1

MATHEMATICA

nn = 8; t = Sum[n^(n - 1) x^n/n!, {n, 1, nn}];

f[list_] := Select[list, # > 0 &];

Map[f, Range[0, nn]! CoefficientList[ Series[Exp[x] Exp[y t], {x, 0, nn}], {x, y}]] // Flatten

CROSSREFS

Cf. A088956, A144289

Sequence in context: A176467 A034802 A177262 * A139167 A211709 A323849

Adjacent sequences:  A203089 A203090 A203091 * A203093 A203094 A203095

KEYWORD

nonn,tabl

AUTHOR

Geoffrey Critzer, Dec 29 2011

STATUS

approved

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Last modified February 27 10:15 EST 2020. Contains 332304 sequences. (Running on oeis4.)