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 A327647 Number of parts in all proper many times partitions of n into distinct parts. 3
 0, 1, 1, 3, 6, 15, 38, 133, 446, 1913, 7492, 36293, 175904, 953729, 5053294, 31353825, 188697696, 1268175779, 8356974190, 61775786301, 448436391810, 3579695446911, 27848806031468, 239229189529685, 2019531300063238, 18477179022470655, 165744369451885256 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS In each step at least one part is replaced by the partition of itself into smaller distinct parts. The parts are not resorted and the parts in the result are not necessarily distinct. LINKS Alois P. Heinz, Table of n, a(n) for n = 0..300 Wikipedia, Partition (number theory) EXAMPLE a(4) = 6 = 1 + 2 + 3, counting the (final) parts in 4, 4->31, 4->31->211. MAPLE b:= proc(n, i, k) option remember; `if`(n=0, [1, 0],      `if`(k=0, [1, 1], `if`(i*(i+1)/2 (f-> f +[0, f[1]*h[2]/h[1]])(h[1]*         b(n-i, min(n-i, i-1), k)))(b(i\$2, k-1)))))     end: a:= n-> add(add(b(n\$2, i)[2]*(-1)^(k-i)*         binomial(k, i), i=0..k), k=0..max(0, n-2)): seq(a(n), n=0..27); CROSSREFS Row sums of A327632, A327648. Sequence in context: A063778 A279374 A087124 * A086326 A098701 A218777 Adjacent sequences:  A327644 A327645 A327646 * A327648 A327649 A327650 KEYWORD nonn AUTHOR Alois P. Heinz, Sep 20 2019 STATUS approved

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Last modified April 3 22:48 EDT 2020. Contains 333207 sequences. (Running on oeis4.)