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A364323 Number of partitions of 2n into n parts 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, 1, 5, 76, 785, 12181, 377708, 8009002, 171155505, 4073421919, 168532394115, 6213455777530, 198071252771780, 6383569557705276, 204582355050315856, 8766238064421938746, 446196770370016437201, 20584924968627941009331, 920598569147050035793061 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
LINKS
FORMULA
a(n) = A364310(2n,n).
EXAMPLE
a(2) = 5: 3abc1d, 3abd1c, 3acd1b, 3bcd1a, 22abcd.
MAPLE
b:= proc(n, i) option remember; expand(`if`(n=0, 1, `if`(i<1, 0,
add(b(n-i*j, i-1)*x^j*binomial(n, i*j), j=0..n/i))))
end:
a:= n-> coeff(b(2*n$2), x, n):
seq(a(n), n=0..23);
MATHEMATICA
b[n_, i_] := b[n, i] = Expand[If[n == 0, 1, If[i < 1, 0,
Sum[b[n - i*j, i - 1]*x^j*Binomial[n, i*j], {j, 0, n/i}]]]];
a[n_] := Coefficient[b[2n, 2n], x, n];
Table[a[n], {n, 0, 23}] (* Jean-François Alcover, Nov 29 2023, from Maple code *)
CROSSREFS
Cf. A364310.
Sequence in context: A258784 A051481 A277296 * A011918 A209095 A136300
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Jul 18 2023
STATUS
approved

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Last modified April 16 10:08 EDT 2024. Contains 371698 sequences. (Running on oeis4.)