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 A276922 Number T(n,k) of ordered set partitions of [n] where the maximal block size equals k; triangle T(n,k), n>=0, 0<=k<=n, read by rows. 13
 1, 0, 1, 0, 2, 1, 0, 6, 6, 1, 0, 24, 42, 8, 1, 0, 120, 330, 80, 10, 1, 0, 720, 2970, 860, 120, 12, 1, 0, 5040, 30240, 10290, 1540, 168, 14, 1, 0, 40320, 345240, 136080, 21490, 2464, 224, 16, 1, 0, 362880, 4377240, 1977360, 326970, 38808, 3696, 288, 18, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 LINKS Alois P. Heinz, Rows n = 0..140, flattened FORMULA E.g.f. for column k>0: 1/(1-Sum_{i=1..k} x^i/i!) - 1/(1-Sum_{i=1..k-1} x^i/i!). T(n,k) = A276921(n,k) - A276921(n,k-1) for k>0. T(n,0) = A000007(0). EXAMPLE Triangle T(n,k) begins:   1;   0,     1;   0,     2,      1;   0,     6,      6,      1;   0,    24,     42,      8,     1;   0,   120,    330,     80,    10,    1;   0,   720,   2970,    860,   120,   12,   1;   0,  5040,  30240,  10290,  1540,  168,  14,  1;   0, 40320, 345240, 136080, 21490, 2464, 224, 16, 1; MAPLE A:= proc(n, k) option remember; `if`(n=0, 1, add(        A(n-i, k)*binomial(n, i), i=1..min(n, k)))     end: T:= (n, k)-> A(n, k) -`if`(k=0, 0, A(n, k-1)): seq(seq(T(n, k), k=0..n), n=0..10); MATHEMATICA A[n_, k_] := A[n, k] = If[n == 0, 1, Sum[A[n - i, k]*Binomial[n, i], {i, 1, Min[n, k]}]]; T[n_, k_] :=  A[n, k] - If[k == 0, 0, A[n, k - 1]]; Table[T[n, k], {n, 0, 10}, { k, 0, n}] // Flatten (* Jean-François Alcover, Feb 11 2017, translated from Maple *) CROSSREFS Columns k=0-10 give: A000007, A000142 (for n>0), A320758, A320759, A320760, A320761, A320762, A320763, A320764, A320765, A320766. Row sums give A000670. T(2n,n) gives A276923. Cf. A080510, A276921. Sequence in context: A111184 A111596 A271703 * A129062 A281662 A163936 Adjacent sequences:  A276919 A276920 A276921 * A276923 A276924 A276925 KEYWORD nonn,tabl AUTHOR Alois P. Heinz, Sep 22 2016 STATUS approved

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Last modified February 19 19:21 EST 2020. Contains 332047 sequences. (Running on oeis4.)