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A375693
Number of multiset permutations of {{1}^n, {2}^n, ..., {n}^n} with no fixed n-tuple {j}^n.
3
1, 0, 5, 1622, 62924817, 623302086965044, 2670169511426774520697375, 7363615066099523741730150062678073534, 18165723898797467057177720588121375861340650728031233, 53130688704554689391452744667655289291011354800478739192999936981375688
OFFSET
0,3
LINKS
FORMULA
a(n) = Sum_{j=0..n} (-1)^(n-j)*binomial(n,j)*(n*j)!/n!^j.
a(n) mod 2 = 1 - (n mod 2) = A059841(n).
EXAMPLE
a(2) = 5: 1212, 1221, 2112, 2121, 2211.
MAPLE
a:= n-> add((-1)^(n-j)*binomial(n, j)*(n*j)!/n!^j, j=0..n):
seq(a(n), n=0..10);
CROSSREFS
Main diagonal of A375694.
Sequence in context: A366830 A123658 A262628 * A237914 A057199 A198246
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Aug 24 2024
STATUS
approved