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 A262078 Number T(n,k) of partitions of an n-set with distinct block sizes and maximal block size equal to k; triangle T(n,k), k>=0, k<=n<=k*(k+1)/2, read by columns. 4
 1, 1, 1, 3, 1, 4, 10, 60, 1, 5, 15, 140, 280, 1260, 12600, 1, 6, 21, 224, 630, 3780, 34650, 110880, 360360, 2522520, 37837800, 1, 7, 28, 336, 1050, 7392, 74844, 276276, 1513512, 9459450, 131171040, 428828400, 2058376320, 9777287520, 97772875200, 2053230379200 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 LINKS Alois P. Heinz, Columns k = 0..36, flattened EXAMPLE Triangle T(n,k) begins: : 1; :    1; :       1; :       3,  1; :           4,     1; :          10,     5,    1; :          60,    15,    6,    1; :                140,   21,    7,   1; :                280,  224,   28,   8,  1; :               1260,  630,  336,  36,  9,  1; :              12600, 3780, 1050, 480, 45, 10, 1; MAPLE b:= proc(n, i) option remember; `if`(i*(i+1)/2n, 0, binomial(n, i)*b(n-i, i-1))))     end: T:= (n, k)-> b(n, k) -`if`(k=0, 0, b(n, k-1)): seq(seq(T(n, k), n=k..k*(k+1)/2), k=0..7); MATHEMATICA b[n_, i_] := b[n, i] = If[i*(i+1)/2n, 0, Binomial[n, i]*b[n-i, i-1]]]]; T[n_, k_] :=  b[n, k] - If[k==0, 0, b[n, k-1]]; Table[T[n, k], {k, 0, 7}, {n, k, k*(k+1)/2}] // Flatten (* Jean-François Alcover, Dec 18 2016, after Alois P. Heinz *) CROSSREFS Row sums give A007837. Column sums give A262073. Cf. A000217, A002024, A262071, A262072 (same read by rows). Sequence in context: A137405 A322456 A301701 * A121922 A054631 A180063 Adjacent sequences:  A262075 A262076 A262077 * A262079 A262080 A262081 KEYWORD nonn,tabf AUTHOR Alois P. Heinz, Sep 10 2015 STATUS approved

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Last modified September 28 11:24 EDT 2020. Contains 337393 sequences. (Running on oeis4.)