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A144259 Number of forests of trees on n or fewer nodes using a subset of labels 1..n, also row sums of triangle A144258. 2
1, 2, 5, 17, 83, 577, 5425, 65221, 959145, 16703045, 336294539, 7687013743, 196668883339, 5568107204467, 172833125462925, 5836126964882633, 212987232417299345, 8353651173273885025, 350415859403143234243, 15654265239209850186247, 741991467954126579131811 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
LINKS
FORMULA
a(n) = Sum_{k=0..n} A144258(n,k).
EXAMPLE
a(2) = 5, because there are 5 forests of trees on 2 or fewer nodes using a subset of labels 1,2:
..... ..... ..... ..... .....
..... .1... ...2. .1.2. .1-2.
..... ..... ..... ..... .....
MAPLE
T:= proc(n, k) option remember; if k=0 then 2^n elif k<0 or n<=k then 0 elif k=n-1 then n^(n-2) else add(binomial(n-1, j) *T(j+1, j) *T(n-1-j, k-j), j=0..k) fi end: a:= n-> add(T(n, k), k=0..n): seq(a(n), n=0..20);
MATHEMATICA
T[n_, k_] := T[n, k] = Which[k==0, 2^n, k<0 || n <= k, 0, k==n-1, n^(n-2), True, Sum[Binomial[n-1, j]*T[j+1, j]*T[n-1-j, k-j], {j, 0, k}]]; a[n_] := Sum[T[n, k], {k, 0, n}]; Table[a[n], {n, 0, 20}] (* Jean-François Alcover, Feb 25 2017, translated from Maple *)
CROSSREFS
Sequence in context: A079574 A363002 A032262 * A191799 A079805 A162038
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Sep 16 2008
STATUS
approved

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Last modified June 15 16:06 EDT 2024. Contains 373407 sequences. (Running on oeis4.)