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

%I

%S 1,1,2,5,14,51,187,820,3670,18191,97917,554500,3334465,20871592,

%T 138440031,972083845,6985171390,52194795327,412903730293,

%U 3313067916192,28017395030419,241504438776956,2189375704925081,19771679215526507,187677937412341677

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

%H Alois P. Heinz, <a href="/A115275/b115275.txt">Table of n, a(n) for n = 0..626</a>

%F 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]

%p with(combinat):

%p b:= proc(n, i) option remember; `if`(n=0, 1,

%p `if`(i<1, 0, add(multinomial(n, n-i*j, i$j)/j!*

%p b(n-i*j, i-1), j=0..min(3, n/i))))

%p end:

%p a:= n-> b(n$2):

%p seq(a(n), n=0..25); # _Alois P. Heinz_, Sep 17 2015

%t 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-Fran├žois Alcover_, Oct 29 2015, after _Alois P. Heinz_ *)

%Y Cf. A001935, A007837, A115276, A115277.

%K nonn

%O 0,3

%A _Christian G. Bower_, Jan 18 2006

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Last modified February 22 19:49 EST 2019. Contains 320403 sequences. (Running on oeis4.)