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A333061 Number of entries in the fourth blocks of all set partitions of [n] when blocks are ordered by decreasing lengths. 2
1, 11, 81, 512, 3151, 20071, 133853, 924320, 6551293, 47529561, 354259153, 2725545695, 21741995463, 180198265559, 1551865576121, 13865702570254, 128238585735637, 1224733005946425, 12053244176971825, 122035994844818345, 1269623551116437475, 13561114665253219451 (list; graph; refs; listen; history; text; internal format)
OFFSET
4,2
LINKS
MAPLE
b:= proc(n, i, t) option remember; `if`(n=0, [1, 0], `if`(i<1, 0,
add((p-> p+`if`(t>0 and t-j<1, [0, p[1]*i], 0))(
combinat[multinomial](n, i$j, n-i*j)/j!*
b(n-i*j, min(n-i*j, i-1), max(0, t-j))), j=0..n/i)))
end:
a:= n-> b(n$2, 4)[2]:
seq(a(n), n=4..25);
MATHEMATICA
multinomial[n_, k_List] := n!/Times @@ (k!);
b[n_, i_, t_] := b[n, i, t] = If[n == 0, {1, 0}, If[i < 1, {0, 0},
Sum[Function[p, p + If[t > 0 && t - j < 1, {0, p[[1]]*i}, {0, 0}]][
multinomial[n, Append[Table[i, {j}], n - i*j]]/j!*
b[n - i*j, Min[n - i*j, i - 1], Max[0, t - j]]], {j, 0, n/i}]]];
a[n_] := b[n, n, 4][[2]];
a /@ Range[4, 25] (* Jean-François Alcover, Apr 24 2021, after Alois P. Heinz *)
CROSSREFS
Column k=4 of A319375.
Sequence in context: A210064 A323223 A211557 * A055429 A227556 A181989
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Mar 06 2020
STATUS
approved

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Last modified June 23 20:00 EDT 2024. Contains 373653 sequences. (Running on oeis4.)