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A350683
Total sum over all partitions of [n] of elements i contained in block i when blocks are ordered with decreasing largest elements.
2
0, 1, 1, 8, 17, 98, 362, 1916, 9512, 53858, 315872, 1984979, 13105685, 91128546, 663815424, 5055622309, 40148341135, 331753228115, 2846786927873, 25323311882074, 233137061978065, 2218141402504254, 21780561656373552, 220451321425101091, 2297330116404668422
OFFSET
0,4
LINKS
FORMULA
a(n) = Sum_{k=1..max(0,A008805(n-1))} k * A350684(n,k).
EXAMPLE
a(4) = 17 = 3*1 + 4*2 + 2*3: 432(1), 42(1)|3, 4(1)|3|2, 43|(2)1, 43|(2)|1, 4|3(2)1, 4|3(2)|1, 43(1)|(2), 4(1)|3(2).
MAPLE
b:= proc(n, m) option remember; `if`(n=0, [1, 0], add((p-> [0,
`if`(n=j, p[1]*j, 0)]+p)(b(n-1, max(m, j))), j=1..m+1))
end:
a:= n-> b(n, 0)[2]:
seq(a(n), n=0..25);
MATHEMATICA
b[n_, m_] := b[n, m] = If[n == 0, {1, 0}, Sum[With[{p = b[n-1, Max[m, j]]},
{0, If[n == j, p[[1]]*j, 0]} + p], {j, 1, m+1}]];
a[n_] := b[n, 0][[2]];
Table[a[n], {n, 0, 25}]; (* Jean-François Alcover, May 08 2022, after Alois P. Heinz *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Jan 11 2022
STATUS
approved