STATUS
reviewed
approved
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Revision History for A370945
(Bold, blue-underlined text is an addition; faded, red-underlined text is aShowing entries 1-10 | older changes
Number T(n,k) of partitions of [n] whose singletons sum to k; triangle T(n,k), n>=0, 0<=k<=A000217(n), read by rows.
(history; published version)
(history; published version)
STATUS
proposed
reviewed
STATUS
editing
proposed
MATHEMATICA
h[n_] := h[n] = If[n == 0, 1,
Sum[h[n-j]*Binomial[n-1, j-1], {j, 2, n}]];
b[n_, i_, m_] := b[n, i, m] = If[n > i*(i + 1)/2, 0,
If[n == 0, h[m], b[n, i - 1, m] + b[n - i, Min[n - i, i - 1], m - 1]]];
T[n_, k_] := b[k, Min[n, k], n];
Table[Table[T[n, k], { k, 0, n*(n + 1)/2}], {n, 0, 7}] // Flatten (* Jean-François Alcover, Mar 12 2024, after Alois P. Heinz *)
STATUS
approved
editing
STATUS
editing
approved
LINKS
Alois P. Heinz, <a href="/A370945/b370945_1.txt">Rows n = 0..50, flattened</a>
STATUS
editing
approved
CROSSREFS
T(n,n) gives A370947.