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 A189940 Number of connected components in all simple labeled graphs with n nodes having degrees at most one. 1
 1, 3, 9, 28, 90, 306, 1078, 3984, 15228, 60580, 248556, 1055088, 4606264, 20712888, 95550120, 452450176, 2193051408, 10882018224, 55166645008, 285683655360, 1508969248416, 8127210649888, 44582377997664, 249000413522688, 1414657929227200, 8172653475494976 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Equivalently, a(n) is the number of cycles in all self-inverse permutations of {1,2,...,n}. LINKS Alois P. Heinz, Table of n, a(n) for n = 1..300 FORMULA E.g.f.: B(A(x)) where A(x) = x +x^2/2 and B(x) = x*exp(x). EXAMPLE a(3) = 9 because the self inverse permutations of [3] are (given in their cycle notation): (1)(2)(3), (1)(2,3), (2)(1,3), (3)(1,2) and there are 9 cycles in all. MAPLE A:= x-> x*(x+2)/2: B:= x-> x*exp(x): a:= n-> n! *coeff(series(B(A(x)), x, n+1), x, n): seq(a(n), n=1..30);  # Alois P. Heinz, May 01 2011 # second Maple program: a:= proc(n) option remember; `if`(n<5, [0, 1, 3, 9, 28][n+1],       (n*(n-5)*a(n-1)+n*(n-1)*(n-3)*a(n-2))/((n-1)*(n-4)))     end: seq(a(n), n=1..30);  # Alois P. Heinz, Feb 10 2014 MATHEMATICA a= x+x^2/2; Drop[Range[0, 20]! CoefficientList[Series[a Exp[a], {x, 0, 20}], x], 1] CROSSREFS Cf. A000085. Sequence in context: A071724 A000245 A143739 * A047047 A071744 A071748 Adjacent sequences:  A189937 A189938 A189939 * A189941 A189942 A189943 KEYWORD nonn AUTHOR Geoffrey Critzer, May 01 2011 STATUS approved

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Last modified January 16 19:49 EST 2019. Contains 319206 sequences. (Running on oeis4.)