A333063 Number of entries in the sixth blocks of all set partitions of [n] when blocks are ordered by decreasing lengths.

1, 22, 295, 3145, 29503, 256565, 2144517, 17743090, 148599335, 1276302900, 11282648837, 102385155537, 949462521827, 8967298797097, 86161326118467, 843025151446964, 8418457337349711, 86033922399717781, 902026616406147607, 9718711403938257151

Offset: 6

Author

Alois P. Heinz, Mar 06 2020

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 6..576
• Wikipedia, Partition of a set

Crossrefs

Column k=6 of A319375.

Programs

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, 6)[2]:
seq(a(n), n=6..25);