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 A144643 Triangle read by rows: T(n,k) = number of partitions of [1..k] into n nonempty clumps of sizes 1, 2, 3 or 4 (n >= 0, 0 <= k <= 4n). 6
 1, 0, 1, 1, 1, 1, 0, 0, 1, 3, 7, 15, 25, 35, 35, 0, 0, 0, 1, 6, 25, 90, 280, 770, 1855, 3675, 5775, 5775, 0, 0, 0, 0, 1, 10, 65, 350, 1645, 6930, 26425, 90475, 275275, 725725, 1576575, 2627625, 2627625, 0, 0, 0, 0, 0, 1, 15, 140, 1050, 6825, 39795 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,10 LINKS Moa Apagodu, David Applegate, N. J. A. Sloane, and Doron Zeilberger, Analysis of the Gift Exchange Problem, arXiv:1701.08394, 2017. David Applegate and N. J. A. Sloane, The Gift Exchange Problem (arXiv:0907.0513, 2009) FORMULA For recurrence see Maple code. EXAMPLE Triangle begins: 1, 0, 1, 1, 1, 1, 0, 0, 1, 3, 7, 15, 25, 35, 35, 0, 0, 0, 1, 6, 25, 90, 280, 770, 1855, 3675, 5775, 5775, 0, 0, 0, 0, 1, 10, 65, 350, 1645, 6930, 26425, 90475, 275275, 725725, 1576575, 2627625, 2627625 0, 0, 0, 0, 0, 1, 15, 140, 1050, 6825, 39795, 211750, 1033725, 4629625, 18918900, 69719650, 227727500, 640264625, 1474097625, 2546168625, 2546168625 MAPLE T := proc(n, k) option remember; if n = k then 1; elif k < n then 0; elif n < 1 then 0; else T(n - 1, k - 1) + (k - 1)*T(n - 1, k - 2) + 1/2*(k - 1)*(k - 2)*T(n - 1, k - 3) + 1/6*(k - 1)*(k - 2)*(k - 3)*T(n - 1, k - 4); end if; end proc; MATHEMATICA T[n_, k_] := T[n, k] = Which[n == k, 1, k

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Last modified May 25 10:57 EDT 2020. Contains 334592 sequences. (Running on oeis4.)