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 A208437 Triangular array read by rows: T(n,k) is the number of set partitions of {1,2,...,n} that have exactly k distinct block sizes. 6
 1, 2, 2, 3, 5, 10, 2, 50, 27, 116, 60, 2, 560, 315, 142, 1730, 2268, 282, 6123, 14742, 1073, 30122, 72180, 12600, 2, 116908, 464640, 97020, 32034, 507277, 2676366, 997920, 2, 2492737, 16400098, 8751600, 136853, 15328119, 94209206, 81225144, 1527528, 56182092, 673282610, 614128515, 37837800 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Column 1 = A038041. Column 2 = A088142. Column 3 = A133118. Row sums = A000110 (Bell numbers). Row n has floor([sqrt(1+8n)-1]/2) terms (number of terms increases by one at each triangular number). - Franklin T. Adams-Watters, Feb 26 2012 LINKS Alois P. Heinz, Rows n = 1..220, flattened Philippe Flajolet and Robert Sedgewick, Analytic Combinatorics, Cambridge Univ. Press, 2009, page 180. FORMULA E.g.f.: Product_{i>=1} 1 + y *(exp(x^i/i!)-1). T(n*(n+1)/2,n) = A022915(n). - Alois P. Heinz, Apr 08 2016 EXAMPLE :    1; :    2; :    2,      3; :    5,     10; :    2,     50; :   27,    116,     60; :    2,    560,    315; :  142,   1730,   2268; :  282,   6123,  14742; : 1073,  30122,  72180,   12600; MAPLE with(combinat): b:= proc(n, i) option remember; expand(`if`(n=0, 1,       `if`(i<1, 0, add(multinomial(n, n-i*j, i\$j)/j!*       b(n-i*j, i-1)*`if`(j=0, 1, x), j=0..n/i))))     end: T:= n-> (p-> seq(coeff(p, x, i), i=1..degree(p)))(b(n\$2)): seq(T(n), n=1..16);  # Alois P. Heinz, Aug 21 2014 MATHEMATICA nn = 15; p = Product[1 + y (Exp[x^i/i!] - 1), {i, 1, nn}]; f[list_] := Select[list, # > 0 &]; Map[f, Drop[ Range[0, nn]! CoefficientList[Series[p, {x, 0, nn}], {x, y}], 1]] // Flatten CROSSREFS Cf. A022915, A116608, A218868. Sequence in context: A153931 A214049 A273034 * A130377 A260956 A322113 Adjacent sequences:  A208434 A208435 A208436 * A208438 A208439 A208440 KEYWORD nonn,tabf AUTHOR Geoffrey Critzer, Feb 26 2012 STATUS approved

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Last modified January 23 16:48 EST 2020. Contains 331173 sequences. (Running on oeis4.)