

A115275


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


3



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
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OFFSET

0,3


LINKS

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


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]


MAPLE

with(combinat):
b:= proc(n, i) option remember; `if`(n=0, 1,
`if`(i<1, 0, add(multinomial(n, ni*j, i$j)/j!*
b(ni*j, i1), 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[{ni*j}, Array[i&, j]]]/j!*b[n  i*j, i1], {j, 0, Min[3, n/i]}]]]; a[n_] := b[n, n]; Table[a[n], {n, 0, 25}] (* JeanFrançois Alcover, Oct 29 2015, after Alois P. Heinz *)


CROSSREFS

Cf. A001935, A007837, A115276, A115277.
Sequence in context: A000109 A049338 A306892 * A000679 A266932 A243787
Adjacent sequences: A115272 A115273 A115274 * A115276 A115277 A115278


KEYWORD

nonn


AUTHOR

Christian G. Bower, Jan 18 2006


STATUS

approved



