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 A215853 Number of simple labeled graphs on n nodes with exactly 3 connected components that are trees or cycles. 3
 1, 6, 55, 540, 6412, 90734, 1515097, 29368155, 649910349, 16178495157, 447436384356, 13607804913248, 451277483034618, 16204761730619392, 626327433705523558, 25924177756443661632, 1144012780063556028591, 53615833082093775740400, 2659498185704802765924159 (list; graph; refs; listen; history; text; internal format)
 OFFSET 3,2 LINKS Alois P. Heinz, Table of n, a(n) for n = 3..145 FORMULA a(n) ~ c * n^(n-2), where c = 0.130848879059... . - Vaclav Kotesovec, Sep 07 2014 EXAMPLE a(4) = 6: .1-2. .1 2. .1 2. .1 2. .1 2. .1 2. . . . |. . . .| . . \ . . / . .4 3. .4 3. .4-3. .4 3. .4 3. .4 3. MAPLE T:= proc(n, k) option remember; `if`(k<0 or k>n, 0, `if`(n=0, 1, add(binomial(n-1, i)*T(n-1-i, k-1)* `if`(i<2, 1, i!/2 +(i+1)^(i-1)), i=0..n-k))) end: a:= n-> T(n, 3): seq(a(n), n=3..25); MATHEMATICA T[n_, k_] := T[n, k] = If[k<0 || k>n, 0, If[n == 0, 1, Sum[Binomial[n-1, i]*T[n-1-i, k-1]*If[i<2, 1, i!/2 + (i+1)^(i-1)], {i, 0, n-k}]]]; a[n_] := T[n, 3]; Table[a[n], {n, 3, 25}] (* Jean-François Alcover, Apr 01 2017, translated from Maple *) CROSSREFS Column k=3 of A215861. The unlabeled version is A215983. Sequence in context: A318592 A342388 A253475 * A110431 A121661 A118836 Adjacent sequences: A215850 A215851 A215852 * A215854 A215855 A215856 KEYWORD nonn AUTHOR Alois P. Heinz, Aug 25 2012 STATUS approved

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Last modified June 9 11:22 EDT 2023. Contains 363178 sequences. (Running on oeis4.)