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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. 2
1, 1, 7, 81, 841, 10333, 137677, 1973401, 29150551, 484498301, 8769443541, 167200081777, 3311785261513, 66867027890601, 1437872937193801, 33031740883673521, 796918495251727081, 19807865344255857661, 501642119664087055501, 12828972405814319046601 (list; graph; refs; listen; history; text; internal format)
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
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
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Jul 18 2023
STATUS
approved

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Last modified May 21 12:49 EDT 2024. Contains 372736 sequences. (Running on oeis4.)