The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A106834 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A106834

Triangle read by rows: T(n, m) = number of painted forests on labeled vertex set [n] with m trees. Also number of painted forests with exactly n - m edges.
(history; published version)

#16 by Bruno Berselli at Wed Feb 25 05:29:08 EST 2015

STATUS

proposed

approved

#15 by Michel Marcus at Wed Feb 25 05:07:18 EST 2015

STATUS

editing

proposed

#14 by Michel Marcus at Wed Feb 25 05:03:20 EST 2015

LINKS

Washington Bomfim, <a href="http://webonfim.vilabol.uol.com.br/A106241.html">Illustration Of This Sequence.</a> [Broken link?]

STATUS

proposed

editing

#13 by Jean-François Alcover at Wed Feb 25 04:58:27 EST 2015

STATUS

editing

proposed

#12 by Jean-François Alcover at Wed Feb 25 04:58:20 EST 2015

MATHEMATICA

f[n_, m_] := f[n, m] = Which[n<0, 0, n == m, 1, m<1 || m>n, 0, True, Sum[ Binomial[n-1, j-1]*j^(j-2)*f[n-j, m-1], {j, 1, n-m+1}]]; T[n_, m_] := m*f[n, m]; Table[Table[T[n, m], {m, 1, n}], {n, 1, 12}] // Flatten (* Jean-François Alcover, Feb 25 2015, after Alois P. Heinz *)

STATUS

approved

editing

#11 by Alois P. Heinz at Mon Dec 29 19:31:30 EST 2014

STATUS

editing

approved

#10 by Alois P. Heinz at Mon Dec 29 19:31:26 EST 2014

MAPLE

f:= proc(n, m) option remember; if n<0 then 0 elif n=m then 1 elif m<1 or m>n then 0 else add (binomial (n-1, j-1) *j^(j-2) *f(n-j, m-1), j=1..n-m+1) fi end: T:= (n, m)-> m*f(n, m): seq (seq (T(n, m), m=1..n), n=1..12); # Alois P. Heinz, Sep 10 2008

f:= proc(n, m) option remember;

if n<0 then 0

elif n=m then 1

elif m<1 or m>n then 0

else add(binomial(n-1, j-1) *j^(j-2) *f(n-j, m-1), j=1..n-m+1)

fi

end:

T:= (n, m)-> m*f(n, m):

seq(seq(T(n, m), m=1..n), n=1..12); # Alois P. Heinz, Sep 10 2008

STATUS

approved

editing

#9 by Charles R Greathouse IV at Fri May 10 12:45:42 EDT 2013

FORMULA

E.g.f.: y*B(x)*exp(y*B(x)), where B(x) is e.g.f. for A000272. - _Vladeta Jovovic (vladeta(AT)eunet.rs), _, May 24 2005

Discussion

Fri May 10

12:45

OEIS Server: https://oeis.org/edit/global/1911

#8 by Alois P. Heinz at Mon Oct 08 16:50:22 EDT 2012

STATUS

editing

approved

#7 by Alois P. Heinz at Mon Oct 08 16:50:14 EDT 2012

LINKS

Washington Bomfim, <a href="http://webonfim.vilabol.uol.com.br/A106241.html">Illustration Of This Sequence.</a>