A367469 a(n) is the total number of movable letters in all members of the partitions of [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
Offset: 1
Keywords
Links
- Toufik Mansour and Mark Shattuck, Counting set partitions by the number of movable letters, Journal of Difference Equations and Applications, 26:3, 384-403, (2020). On ResearchGate. See Theorem 8.
Programs
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Mathematica
a[n_]:=(2n-1)BellB[n]/2-BellB[n+1]/2+BellB[n-1]/2; Array[a,24]
Formula
a(n) = (2*n - 1)*B(n)/2 - B(n+1)/2 + B(n-1)/2, where B(n) = A000110(n).