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A327645 Number of proper n-times partitions of 2n. 2

%I

%S 1,1,6,88,2489,112669,8204101,799422247,109633217402,19157475773052,

%T 4260985739868007,1161511740640164091,388990633971649889649,

%U 152369510393132343133762,70914541309488196549283707,38152280583855500772704976704,23639325145221113389859164367779

%N Number of proper n-times partitions of 2n.

%C In each step at least one part is replaced by the partition of itself into smaller parts. The parts are not resorted.

%H Alois P. Heinz, <a href="/A327645/b327645.txt">Table of n, a(n) for n = 0..232</a>

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

%e a(2) = 6: 4->31->211, 4->31->1111, 4->22->112, 4->22->211, 4->22->1111, 4->211->1111.

%p b:= proc(n, i, k) option remember; `if`(n=0 or k=0, 1, `if`(i>1,

%p b(n, i-1, k), 0) +b(i$2, k-1)*b(n-i, min(n-i, i), k))

%p end:

%p a:= n-> add(b(2*n$2, i)*(-1)^(n-i)*binomial(n, i), i=0..n):

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

%Y Cf. A327639.

%K nonn

%O 0,3

%A _Alois P. Heinz_, Sep 20 2019

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Last modified March 28 18:52 EDT 2020. Contains 333103 sequences. (Running on oeis4.)