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A027852
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Number of connected functions on n points with a loop of length 2.
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2
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0, 1, 1, 3, 6, 16, 37, 96, 239, 622, 1607, 4235, 11185, 29862, 80070, 216176, 586218, 1597578, 4370721, 12003882, 33077327, 91433267, 253454781, 704429853, 1962537755, 5479855546, 15332668869, 42983656210, 120716987723, 339596063606, 956840683968
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,4
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COMMENTS
| Also rooted trees on n+1 nodes where root has degree 2.
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LINKS
| Alois P. Heinz, Table of n, a(n) for n = 1..650
Index entries for sequences related to rooted trees
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FORMULA
| G.f.: A(x) = (B(x)^2 + B(x^2))/2 where B(x) is g.f. of A000081.
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MAPLE
| with(numtheory): b:= proc(n) option remember; local d, j; `if` (n<=1, n, (add (add (d*b(d), d=divisors(j)) *b(n-j), j=1..n-1))/ (n-1)) end: a:= n-> (add (b(i) *b(n-i), i=0..n) +`if`(irem (n, 2)=0, b(n/2), 0))/2: seq (a(n), n=1..50); # Alois P. Heinz, Aug 22 2008, revised Oct 07 2011
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CROSSREFS
| Cf. A000081, A000226, A001372, A002861.
Sequence in context: A130095 A072824 A089406 * A203068 A114410 A190735
Adjacent sequences: A027849 A027850 A027851 * A027853 A027854 A027855
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KEYWORD
| nonn
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AUTHOR
| Christian G. Bower (bowerc(AT)usa.net), Dec 14 1997
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EXTENSIONS
| Edited by Christian G. Bower (bowerc(AT)usa.net), Feb 12 2002
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