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A282988 Triangle of partitions of an n-set into boxes of size >= m. 2
1, 2, 1, 5, 1, 1, 15, 4, 1, 1, 52, 11, 1, 1, 1, 203, 41, 11, 1, 1, 1, 877, 162, 36, 1, 1, 1, 1, 4140, 715, 92, 36, 1, 1, 1, 1, 21147, 3425, 491, 127, 1, 1, 1, 1, 1, 115975, 17722, 2557, 337, 127, 1, 1, 1, 1, 1, 678570, 98253, 11353, 793, 463, 1, 1, 1, 1, 1, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
1,2
LINKS
FORMULA
T(n,m) = Sum_{i=0..n-m} C(n-1, i+m-1)*T(n-i-m, m).
E.g.f. m column of T(n,m) is exp(exp(x)-Sum_{k=0..m} 1/k!x^k).
EXAMPLE
Triangle T(n,m) begins:
1;
2, 1;
5, 1, 1;
15, 4, 1, 1;
52, 11, 1, 1, 1;
203, 41, 11, 1, 1, 1;
877, 162, 36, 1, 1, 1, 1;
...
MAPLE
T:= proc(n, k) option remember; `if`(n=0, 1, add(
T(n-j, k)*binomial(n-1, j-1), j=k..n))
end:
seq(seq(T(n, k), k=1..n), n=1..14); # Alois P. Heinz, Sep 28 2017
MATHEMATICA
T[n_, m_] := T[n, m] = Which[Or[n == m, n == 0], 1, m == 0, 0, True, Sum[Binomial[n - 1, i + m - 1] T[n - i - m, m], {i, 0, n - m}]]; Table[T[n, m], {n, 11}, {m, n}] // Flatten (* Michael De Vlieger, Feb 26 2017 *)
PROG
(Maxima)
T(n, m):=if n=m or n=0 then 1 else if m=0 then 0 else sum(binomial(n-1, i+m-1)*T(n-i-m, m), i, 0, n-m);
CROSSREFS
Sequence in context: A299779 A323954 A143983 * A113767 A352566 A246964
KEYWORD
nonn,tabl
AUTHOR
Vladimir Kruchinin, Feb 26 2017
STATUS
approved

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Last modified April 24 04:14 EDT 2024. Contains 371918 sequences. (Running on oeis4.)