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A327645 Number of proper n-times partitions of 2n. 2
1, 1, 6, 88, 2489, 112669, 8204101, 799422247, 109633217402, 19157475773052, 4260985739868007, 1161511740640164091, 388990633971649889649, 152369510393132343133762, 70914541309488196549283707, 38152280583855500772704976704, 23639325145221113389859164367779 (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..232

FORMULA

a(n) = A327639(2n,n).

EXAMPLE

a(2) = 6: 4->31->211, 4->31->1111, 4->22->112, 4->22->211, 4->22->1111, 4->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(b(2*n$2, i)*(-1)^(n-i)*binomial(n, i), i=0..n):

seq(a(n), n=0..17);

CROSSREFS

Cf. A327639.

Sequence in context: A177567 A177563 A177569 * A309165 A127183 A054952

Adjacent sequences:  A327642 A327643 A327644 * A327646 A327647 A327648

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.)