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 A327648 Number of parts in all proper many times partitions of n. 4
 0, 1, 3, 9, 45, 185, 1277, 7469, 67993, 514841, 5414197, 52609653, 679432169, 7704502013, 111283754969, 1515535050805, 25257251330321, 385282195339393, 7088110874426409, 123325149268482781, 2520808658222616653, 48623257343586890769, 1078165538033926164281 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS In each step at least one part is replaced by the partition of itself into smaller parts. The parts are not resorted. LINKS Alois P. Heinz, Table of n, a(n) for n = 0..300 Wikipedia, Partition (number theory) EXAMPLE a(3) = 9 = 1 + 2 + 3 + 3, counting the (final) parts in: 3, 3->21, 3->111, 3->21->111. a(4) = 45: 4, 4->31, 4->22, 4->211, 4->1111, 4->31->211, 4->31->1111, 4->22->112, 4->22->211, 4->22->1111, 4->211->1111, 4->31->211->1111, 4->22->112->1111, 4->22->211->1111. MAPLE b:= proc(n, i, k) option remember; `if`(n=0, [1, 0],      `if`(k=0, [1, 1], `if`(i<2, 0, b(n, i-1, k))+          (h-> (f-> f +[0, f[1]*h[2]/h[1]])(h[1]*         b(n-i, min(n-i, i), 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..n-1): seq(a(n), n=0..25); CROSSREFS Row sums of A327631. Cf. A327644, A327647. Sequence in context: A224085 A192891 A068100 * A262129 A012821 A229813 Adjacent sequences:  A327645 A327646 A327647 * A327649 A327650 A327651 KEYWORD nonn AUTHOR Alois P. Heinz, Sep 20 2019 STATUS approved

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Last modified April 4 20:53 EDT 2020. Contains 333229 sequences. (Running on oeis4.)