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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.

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Cf. A000110.

Cf. A000110.Row sums of A367468.

allocateda(n) is the total number of movable letters in all members of forthe Stefanopartitions Speziaof [n].

0, 1, 6, 29, 140, 704, 3732, 20915, 123832, 773051, 5076174, 34973432, 252212600, 1899483793, 14908277490, 121701247649, 1031472019760, 9061405440156, 82384690078948, 774102548613907, 7507335441107420, 75055820357153647, 772694054961218802, 8182814265240466788

1,3

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). See Theorem 8.

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

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

Cf. A000110.Row sums of A367468.

allocated

nonn

Stefano Spezia, Nov 19 2023

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allocated for Stefano Spezia

allocated

approved