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A103194
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LAH transform of squares.
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2
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0, 1, 6, 39, 292, 2505, 24306, 263431, 3154824, 41368977, 589410910, 9064804551, 149641946796, 2638693215769, 49490245341642, 983607047803815, 20646947498718736, 456392479671188001, 10595402429677269174, 257723100178182605287, 6553958557721713088820
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OFFSET
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0,3
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COMMENTS
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If the E.g.f. of b(n) is E(x) and a(n) = Sum{k=0..n} C(n,k)^2*(n-k)!*b(k), then the E.g.f. of a(n) is E(x/(1-x))/(1-x). [Vladeta Jovovic, Apr 16 2005]
a(n) is the total number of elements in all partial permutations (injective partial functions) of {1,2,...,n} that are in a cycle. A fixed point is considered to be in a cycle. a(n) = Sum_{k=0..n} A206703(n,k)*k. - Geoffrey Critzer, Feb 11 2012.
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REFERENCES
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Philippe Flajolet and Robert Sedgewick, Analytic Combinatorics, Cambridge Univ. Press, 2009, page 132.
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LINKS
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Alois P. Heinz, Table of n, a(n) for n = 0..200
N. J. A. Sloane, Transforms
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FORMULA
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a(n) = Sum_{k=0..n} n!/k!*binomial(n-1, k-1)*k^2. E.g.f.: x/(1-x)^2*exp(x/ (1-x)). Recurrence: (n-1)*a(n)-n*(2*n-1)*a(n-1)+n*(n-1)^2*a(n-2) = 0.
a(n) = n*A000262(n). - Vladeta Jovovic, Mar 20 2005
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MAPLE
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with(combstruct): SetSeqSetL := [T, {T=Set(S), S=Sequence(U, card >= 1), U=Set(Z, card=1)}, labeled]: seq(k*count(SetSeqSetL, size=k), k=0..18); # Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 06 2007
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MATHEMATICA
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nn = 20; a = 1/(1 - x); ay = 1/(1 - y x); D[Range[0, nn]! CoefficientList[ Series[Exp[a x] ay, {x, 0, nn}], x], y] /. y -> 1 (* Geoffrey Critzer, Feb 11 2012 *)
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CROSSREFS
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Cf. A001477.
Sequence in context: A006633 A153392 A122827 * A009018 A135890 A067273
Adjacent sequences: A103191 A103192 A103193 * A103195 A103196 A103197
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KEYWORD
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easy,nonn,changed
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AUTHOR
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Vladeta Jovovic, Mar 18 2005
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STATUS
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approved
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