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A327646 Total number of steps in all proper many times partitions of n. 2
0, 0, 1, 4, 25, 108, 788, 4740, 44445, 339632, 3625136, 35508536, 462626736, 5273725108, 76634997096, 1047347436984, 17542238923677, 268193251446228, 4949536256552648, 86303019303031400, 1768833677916545596, 34165810747993948664, 759192269597947084836 (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 parts. The parts are not resorted.

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..400

FORMULA

a(n) = Sum_{k=1..n-1} k * A327639(n,k).

EXAMPLE

a(3) = 4 = 0+1+1+2, counting steps "->" in: 3, 3->21, 3->111, 3->21->111.

a(4) = 25: 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(k*add(b(n$2, i)*(-1)^(k-i)*

        binomial(k, i), i=0..k), k=1..n-1):

seq(a(n), n=0..23);

CROSSREFS

Cf. A327639.

Sequence in context: A042651 A225692 A070764 * A244746 A110051 A273023

Adjacent sequences:  A327643 A327644 A327645 * A327647 A327648 A327649

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Sep 20 2019

STATUS

approved

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Last modified February 23 06:13 EST 2020. Contains 332159 sequences. (Running on oeis4.)