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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 June 6 22:19 EDT 2023. Contains 363151 sequences. (Running on oeis4.)