%I #7 Nov 22 2023 22:30:02

%S 0,1,6,29,140,704,3732,20915,123832,773051,5076174,34973432,252212600,

%T 1899483793,14908277490,121701247649,1031472019760,9061405440156,

%U 82384690078948,774102548613907,7507335441107420,75055820357153647,772694054961218802,8182814265240466788

%N a(n) is the total number of movable letters in all members of the partitions of [n].

%H Toufik Mansour and Mark Shattuck, <a href="https://doi.org/10.1080/10236198.2020.1739275">Counting set partitions by the number of movable letters</a>, Journal of Difference Equations and Applications, 26:3, 384-403, (2020). <a href="https://www.researchgate.net/publication/374910923_Counting_set_partitions_by_the_number_of_movable_letters">On ResearchGate</a>. See Theorem 8.

%F a(n) = (2*n - 1)*B(n)/2 - B(n+1)/2 + B(n-1)/2, where B(n) = A000110(n).

%t a[n_]:=(2n-1)BellB[n]/2-BellB[n+1]/2+BellB[n-1]/2; Array[a,24]

%Y Cf. A000110.

%Y Row sums of A367468.

%K nonn

%O 1,3

%A _Stefano Spezia_, Nov 19 2023