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Search: id:A101313
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| A101313 |
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Number of painted forests - exactly one of its trees is painted - on labeled vertex set [n]. |
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+0
2
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| 1, 3, 12, 68, 525, 5262, 65674, 987408, 17426565, 353759300, 8127640224, 208600774032, 5917247520457, 183872561612040, 6212370268252950, 226762373954676608, 8893485959056048521, 372980176625914811568
(list; graph; listen)
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OFFSET
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1,2
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FORMULA
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a(n) = f(n) + SUM{((n-i)^(n-i-2))*C((n-1), i)*a(i):i=1, 2, ..(n-1)}, where f(n)=number of forests on labeled vertex set [n], A001858
Exponential convolution of A000272 and A001858: a(n) = Sum_{k=1..n} binomial(n, k)*k^(k-2)*A001858(n-k). E.g.f.: B(x)*exp(B(x)), where B(x) is e.g.f. for A000272. - Vladeta Jovovic (vladeta(AT)Eunet.yu), May 24 2005
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EXAMPLE
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a(5)=291+{(16*4*1)+(3*6*3)+(1*4*12)+(1*1*68)}=525
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MAPLE
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B:= n-> exp (add (k^(k-2) *x^k/k!, k = 1..n )): b:= n-> coeff (series (B(n), x, n+1) , x, n)*n!: a:= n-> add (binomial(n, k) *k^(k-2) *b(n-k), k=1..n): seq (a(n), n=1..25); [From Alois P. Heinz (heinz(AT)hs-heilbronn.de), Sep 10 2008]
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CROSSREFS
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Sequence in context: A039750 A004127 A058115 this_sequence A144008 A102078 A113341
Adjacent sequences: A101310 A101311 A101312 this_sequence A101314 A101315 A101316
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KEYWORD
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nonn
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AUTHOR
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Joseph G. Moser (jmoser(AT)wcupa.edu), Jan 26 2005
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EXTENSIONS
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More terms from Alois P. Heinz (heinz(AT)hs-heilbronn.de), Sep 10 2008
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