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 A215854 Number of simple labeled graphs on n nodes with exactly 4 connected components that are trees or cycles. 3
 1, 10, 125, 1610, 23597, 394506, 7533445, 163190665, 3971678359, 107502644249, 3205669601953, 104435680520535, 3690517248021753, 140590728463023632, 5743180320999041664, 250423270549658253350, 11608409727652016747176, 570034426072900362961212 (list; graph; refs; listen; history; text; internal format)
 OFFSET 4,2 LINKS Alois P. Heinz, Table of n, a(n) for n = 4..145 EXAMPLE a(4) = 1: the graph with 4 1-node trees. a(5) = 10: each graph has one 2-node tree and 3 1-node trees, and C(5,2) = 10. 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, 4): seq(a(n), n=4..25); CROSSREFS Column k=4 of A215861. The unlabeled version is A215984. Sequence in context: A259839 A005174 A034668 * A123358 A230390 A089832 Adjacent sequences:  A215851 A215852 A215853 * A215855 A215856 A215857 KEYWORD nonn AUTHOR Alois P. Heinz, Aug 25 2012 STATUS approved

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Last modified January 27 09:09 EST 2020. Contains 331293 sequences. (Running on oeis4.)