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 A215863 Number of simple labeled graphs on n+3 nodes with exactly n connected components that are trees or cycles. 2
 0, 19, 135, 540, 1610, 3990, 8694, 17220, 31680, 54945, 90805, 144144, 221130, 329420, 478380, 679320, 945744, 1293615, 1741635, 2311540, 3028410, 3920994, 5022050, 6368700, 8002800, 9971325, 12326769, 15127560, 18438490, 22331160, 26884440, 32184944, 38327520 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Alois P. Heinz, Table of n, a(n) for n = 0..1000 FORMULA G.f.: (6*x^2-2*x-19)*x/(x-1)^7. a(n) = C(n+3,4)*(n^2+13*n+24)/2. EXAMPLE a(1) = 19: .1-2. .1-2. .1 2. .1-2. .1-2. .1 2. .1 2. .1 2. .1-2. .1-2. .| |. . X . .|X|. .|\ . . /|. . \|. .|/ . .| |. .| . .| |. .4-3. .4-3. .4.3. .4.3. .4.3. .4-3. .4-3. .4-3. .4-3. .4.3. . .1-2. .1 2. .1-2. .1-2. .1-2. .1 2. .1 2. .1 2. .1 2. . |. . X . . / . . \ . . X . .|/|. . X|. .|X . .|\|. .4-3. .4-3. .4-3. .4-3. .4.3. .4.3. .4.3. .4.3. .4.3. MAPLE a:= n-> binomial(n+3, 4)*(24+(13+n)*n)/2: seq(a(n), n=0..40); CROSSREFS A diagonal of A215861. Sequence in context: A041692 A078977 A085464 * A101090 A213122 A211092 Adjacent sequences: A215860 A215861 A215862 * A215864 A215865 A215866 KEYWORD nonn AUTHOR Alois P. Heinz, Aug 25 2012 STATUS approved

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Last modified March 1 14:57 EST 2024. Contains 370433 sequences. (Running on oeis4.)