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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
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 (list; graph; refs; listen; history; text; internal format)
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, 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-Fran├žois Alcover, Oct 29 2015, after Alois P. Heinz *)

CROSSREFS

Cf. A001935, A007837, A115276, A115277.

Sequence in context: A298361 A000109 A049338 * A000679 A266932 A243787

Adjacent sequences:  A115272 A115273 A115274 * A115276 A115277 A115278

KEYWORD

nonn

AUTHOR

Christian G. Bower, Jan 18 2006

STATUS

approved

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Last modified February 25 16:14 EST 2018. Contains 299653 sequences. (Running on oeis4.)