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%I #16 Jun 13 2023 15:21:48
%S 1,1,8,122,2795,86472,3403127,164029595,9433737120,635182667816,
%T 49344452550230,4371727233798927,437489737355466560,
%U 49048715505983309703,6116937802946210183545,843220239072837883168510,127757559136845878072576947,21166434937698025552654090472
%N a(n) = A359107(2*n, n) = Sum_{j=0..n} Stirling2(2*n, j) = Sum_{j=0..n} A048993(2*n, j).
%C a(n) is the number of partitions of an 2n-set that contain at most n nonempty subsets.
%H Alois P. Heinz, <a href="/A359355/b359355.txt">Table of n, a(n) for n = 0..288</a>
%F a(n) = A102661(2n,n) for n >= 1. - _Alois P. Heinz_, Jun 13 2023
%p b:= proc(n) option remember; `if`(n=0, 1,
%p add(expand(b(n-j)*binomial(n-1, j-1)*x), j=1..n))
%p end:
%p a:= n-> (p-> add(coeff(p, x, i), i=0..n))(b(2*n, 0)):
%p seq(a(n), n=0..17); # _Alois P. Heinz_, Jun 13 2023
%o (PARI) a(n) = sum(j=0, n, stirling(2*n, j, 2)); \\ _Michel Marcus_, Dec 27 2022
%Y Cf. A359107, A048993, A102661.
%K nonn
%O 0,3
%A _Peter Luschny_, Dec 27 2022