The On-Line Encyclopedia of Integer Sequences (OEIS)

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A240682

Number of forests with n labeled nodes and 5 trees.
(history; published version)

#9 by Vaclav Kotesovec at Sat Sep 06 14:59:17 EDT 2014

STATUS

editing

approved

#8 by Vaclav Kotesovec at Sat Sep 06 14:58:48 EDT 2014

FORMULA

a(n) = n^(n-10) * (n-4)*(n-3)*(n-2)*(n-1)*(n^4 + 30*n^3 + 451*n^2 + 3846*n + 15120)/384. - Vaclav Kotesovec, Sep 06 2014

MATHEMATICA

Table[n^(n-10) * (n-4)*(n-3)*(n-2)*(n-1)*(n^4 + 30*n^3 + 451*n^2 + 3846*n + 15120)/384, {n, 5, 20}] (* Vaclav Kotesovec, Sep 06 2014 *)

STATUS

approved

editing

#7 by Alois P. Heinz at Fri Apr 11 08:25:24 EDT 2014

STATUS

editing

approved

#6 by Alois P. Heinz at Fri Apr 11 08:25:20 EDT 2014

CROSSREFS

Column m=5 of A105599. A diagonal of A138464.

STATUS

approved

editing

#5 by Alois P. Heinz at Thu Apr 10 11:23:50 EDT 2014

STATUS

editing

approved

#4 by Alois P. Heinz at Thu Apr 10 11:23:44 EDT 2014

MAPLE

T:= proc(n, m) option remember; `if`(n<0, 0, `if`(n=m, 1,

`if`(m<1 or m>n, 0, add(binomial(n-1, j-1)*j^(j-2)*

T(n-j, m-1), j=1..n-m+1))))

end:

a:= n-> T(n, 5):

seq(a(n), n=5..30);

#3 by Alois P. Heinz at Thu Apr 10 10:50:57 EDT 2014

LINKS

Alois P. Heinz, <a href="/A240682/b240682.txt">Table of n, a(n) for n = 5..200</a>

#2 by Alois P. Heinz at Thu Apr 10 10:49:32 EDT 2014

NAME

allocated for Alois P. Heinz

Number of forests with n labeled nodes and 5 trees.

DATA

1, 15, 210, 3220, 55755, 1092105, 24048255, 590412240, 16027796070, 477411574640, 15495339234375, 544652100894720, 20619226977792170, 836670560604157440, 36232055577668433690, 1668081561600000000000, 81363801140161673297535, 4191692026268767965880320

OFFSET

5,2

CROSSREFS

Column m=5 of A105599.

KEYWORD

allocated

nonn

AUTHOR

Alois P. Heinz, Apr 10 2014

STATUS

approved

editing

#1 by Alois P. Heinz at Thu Apr 10 10:43:31 EDT 2014

NAME

allocated for Alois P. Heinz

KEYWORD

allocated

STATUS

approved