A364322 Number of partitions of 2n with largest part n where each block of part i with multiplicity j is marked with a word of length i*j over a (2n)-ary alphabet whose letters appear in alphabetical order and all 2n letters occur exactly once in the partition.

1, 1, 7, 81, 841, 10333, 137677, 1973401, 29150551, 484498301, 8769443541, 167200081777, 3311785261513, 66867027890601, 1437872937193801, 33031740883673521, 796918495251727081, 19807865344255857661, 501642119664087055501, 12828972405814319046601

Offset

0,3

Comments

a(n) is also the number of endofunctions on [2n] such that n is the range maximum and the number of elements that are mapped to m is divisible by m. a(2) = 7: (2211), (2121), (2112), (1221), (1212), (1122), (2222).

All terms are odd.

Links

Alois P. Heinz, Table of n, a(n) for n = 0..503

Formula

a(n) = A364285(2n,n).

Example

a(2) = 7: 2ab11cd, 2ac11bd, 2ad11bc, 2bc11ad, 2bd11ac, 2cd11ab, 22abcd.

Maple

b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,
      add(b(n-i*j, i-1)*binomial(n, i*j), j=0..n/i)))
    end:
a:= n-> b(2*n, n)-`if`(n=0, 0, b(2*n, n-1)):
seq(a(n), n=0..23);

Crossrefs

Cf. A364285.

Sequence in context: A050861 A083226 A088735 * A339710 A112119 A369024

Adjacent sequences: A364319 A364320 A364321 * A364323 A364324 A364325

Keyword

nonn

Author

Alois P. Heinz, Jul 18 2023

Status

approved