A319375 -id:A319375 - cp's OEIS frontend

A333066 Number of entries in the ninth blocks of all set partitions of [n] when blocks are ordered by decreasing lengths.

1, 46, 1211, 24047, 401337, 5957407, 81381744, 1046405027, 12866407790, 153103993523, 1780561219354, 20417258320972, 232758457316938, 2658399095977056, 30621521649045981, 357523836553565584, 4243836001737759231, 51265500225372571466, 629904897694885693327

Offset: 9

Alois P. Heinz, Mar 06 2020

nonn

Alois P. Heinz, Table of n, a(n) for n = 9..576
Wikipedia, Partition of a set

Column k=9 of A319375.

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, 9)[2]:
seq(a(n), n=9..27);

A333067 Number of entries in the tenth blocks of all set partitions of [n] when blocks are ordered by decreasing lengths.

Original entry on oeis.org

1, 56, 1772, 41835, 822277, 14253254, 225620777, 3337585487, 46894138343, 633327676249, 8297945378872, 106274752981884, 1339352574256161, 16713308238007881, 207742699406820799, 2586686884152971976, 32427925119758431591, 410991858695177722552

Offset: 10

Alois P. Heinz, Mar 06 2020

nonn

Alois P. Heinz, Table of n, a(n) for n = 10..576
Wikipedia, Partition of a set

Column k=10 of A319375.

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, 10)[2]:
seq(a(n), n=10..27);

cp's OEIS Frontend

A333066 Number of entries in the ninth blocks of all set partitions of [n] when blocks are ordered by decreasing lengths.

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