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 A327644 Number of proper many times partitions of n. 3
 1, 1, 2, 4, 14, 44, 244, 1196, 9366, 62296, 584016, 5120548, 60244028, 627389924, 8378159376, 106097674780, 1652301306958, 23655318730276, 409987534384504, 6742903763089068, 130675390985884516, 2396246933608687036, 50636625943991790784, 1032841246318579471748 (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..400 Vaclav Kotesovec, Plot of a(n+1)/(n*a(n)) for n = 1..400 EXAMPLE a(3) = 4: 3, 3->21, 3->111, 3->21->111. a(4) = 14: 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 or k=0, 1, `if`(i>1,       b(n, i-1, k), 0) +b(i\$2, k-1)*b(n-i, min(n-i, i), k))     end: a:= n-> add(add(b(n\$2, i)*(-1)^(k-i)*         binomial(k, i), i=0..k), k=0..max(0, n-1)): seq(a(n), n=0..23); MATHEMATICA b[n_, i_, k_] := b[n, i, k] = If[n == 0 || k == 0, 1, If[i > 1, b[n, i - 1, k], 0] + b[i, i, k - 1] b[n - i, Min[n - i, i], k]]; a[n_] := Sum[b[n, n, i] (-1)^(k - i) Binomial[k, i], {k, 0, Max[0, n - 1]}, {i, 0, k}]; a /@ Range[0, 23] (* Jean-François Alcover, Dec 09 2020, after Alois P. Heinz *) CROSSREFS Row sums of A327639. Cf. A327648. Sequence in context: A007866 A226909 A121751 * A151355 A014272 A070822 Adjacent sequences:  A327641 A327642 A327643 * A327645 A327646 A327647 KEYWORD nonn AUTHOR Alois P. Heinz, Sep 20 2019 STATUS approved

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Last modified April 17 06:46 EDT 2021. Contains 343059 sequences. (Running on oeis4.)