A115275 Number of partitions of {1,...,n} into blocks such that no block size is repeated more than 3 times.

1, 1, 2, 5, 14, 51, 187, 820, 3670, 18191, 97917, 554500, 3334465, 20871592, 138440031, 972083845, 6985171390, 52194795327, 412903730293, 3313067916192, 28017395030419, 241504438776956, 2189375704925081, 19771679215526507, 187677937412341677

Offset: 0

Author

Christian G. Bower, Jan 18 2006

Keywords

• nonn
• changed

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..626

Crossrefs

Cf. A000110, A001935, A007837, A115276, A115277.

Programs

Maple

with(combinat):
b:= proc(n, i) option remember; `if`(n=0, 1,
      `if`(i<1, 0, add(multinomial(n, n-i*j, i$j)/j!*
      b(n-i*j, i-1), j=0..min(3, n/i))))
    end:
a:= n-> b(n$2):
seq(a(n), n=0..25);  # Alois P. Heinz, Sep 17 2015

Mathematica

multinomial[n_, k_List] := n!/Times @@ (k!); b[n_, i_] := b[n, i] = If[n == 0, 1, If[i<1, 0, Sum[multinomial[n, Join[{n-i*j}, Array[i&, j]]]/j!*b[n - i*j, i-1], {j, 0, Min[3, n/i]}]]]; a[n_] := b[n, n]; Table[a[n], {n, 0, 25}] (* Jean-François Alcover, Oct 29 2015, after Alois P. Heinz *)

Formula

E.g.f.: Product {m >= 1} (1+x^m/m!+(x^m/m!)^2+(x^m/m!)^3). [this e.g.f. is incorrect. - Vaclav Kotesovec, Oct 29 2015]