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A114917
Number of partitions of {1,..,n} in which no part of a given size occurs just once.
3
1, 0, 1, 1, 4, 1, 71, 106, 1051, 2759, 19552, 51041, 864579, 3134132, 34990671, 211464345, 1832236004, 11261632321, 109973219879, 659853699654, 8379292553185, 58134013363151, 676374746166550, 5912498819726335, 71622214447120275, 658455096592878092
OFFSET
0,5
LINKS
MAPLE
b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,
add(`if`(j=1, 0, b(n-i*j, i-1)*combinat[multinomial]
(n, n-i*j, i$j)/j!), j=0..min(n/i))))
end:
a:= n-> b(n$2):
seq(a(n), n=0..26); # Alois P. Heinz, May 14 2023
MATHEMATICA
multinomial[n_, k_List] := n!/Times @@ (k!);
b[n_, i_] := b[n, i] = If[n == 0, 1, If[i < 1, 0, Sum[If[j == 1, 0, b[n - i*j, i - 1]*multinomial[n, Prepend[Table[i, {j}], n - i*j]]/j!], {j, 0, Min[n/i]}]]];
a[n_] := b[n, n];
Table[a[n], {n, 0, 26}] (* Jean-François Alcover, May 26 2023, after Alois P. Heinz *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Christian G. Bower, Jan 06 2006
STATUS
approved