login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo

Thanks to everyone who made a donation during our annual appeal!
To see the list of donors, or make a donation, see the OEIS Foundation home page.

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A319066 Number of partitions of integer partitions of n where all parts have the same length. 30
1, 1, 3, 5, 10, 14, 26, 35, 59, 82, 128, 176, 273, 371, 553, 768, 1119, 1544, 2235, 3084, 4410, 6111, 8649, 11982, 16901, 23383, 32780, 45396, 63365, 87622, 121946, 168407, 233605, 322269, 445723, 613922, 847131, 1164819, 1603431, 2201370, 3023660, 4144124, 5680816 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Andrew Howroyd, Table of n, a(n) for n = 0..500

EXAMPLE

The a(1) = 1 through a(5) = 14 multiset partitions:

  {{1}}  {{2}}      {{3}}          {{4}}              {{5}}

         {{1,1}}    {{1,2}}        {{1,3}}            {{1,4}}

         {{1},{1}}  {{1,1,1}}      {{2,2}}            {{2,3}}

                    {{1},{2}}      {{1,1,2}}          {{1,1,3}}

                    {{1},{1},{1}}  {{1},{3}}          {{1,2,2}}

                                   {{2},{2}}          {{1},{4}}

                                   {{1,1,1,1}}        {{2},{3}}

                                   {{1,1},{1,1}}      {{1,1,1,2}}

                                   {{1},{1},{2}}      {{1,1,1,1,1}}

                                   {{1},{1},{1},{1}}  {{1,1},{1,2}}

                                                      {{1},{1},{3}}

                                                      {{1},{2},{2}}

                                                      {{1},{1},{1},{2}}

                                                      {{1},{1},{1},{1},{1}}

MATHEMATICA

sps[{}]:={{}}; sps[set:{i_, ___}]:=Join@@Function[s, Prepend[#, s]&/@sps[Complement[set, s]]]/@Cases[Subsets[set], {i, ___}];

mps[set_]:=Union[Sort[Sort/@(#/.x_Integer:>set[[x]])]&/@sps[Range[Length[set]]]];

Table[Length[Select[Join@@mps/@IntegerPartitions[n], SameQ@@Length/@#&]], {n, 8}]

PROG

(PARI) EulerT(v)={Vec(exp(x*Ser(dirmul(v, vector(#v, n, 1/n))))-1, -#v)}

seq(n)={my(p=1/prod(k=1, n, 1 - x^k*y + O(x*x^n))); concat([1], sum(k=1, n, EulerT(Vec(polcoef(p, k, y), -n))))} \\ Andrew Howroyd, Oct 25 2018

CROSSREFS

Cf.  A001970, A047968, A261049, A279787, A305551, A306017, A319056.

Sequence in context: A229915 A092269 A323429 * A306319 A182722 A089483

Adjacent sequences:  A319063 A319064 A319065 * A319067 A319068 A319069

KEYWORD

nonn

AUTHOR

Gus Wiseman, Oct 10 2018

EXTENSIONS

Terms a(11) and beyond from Andrew Howroyd, Oct 25 2018

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified January 23 10:36 EST 2020. Contains 331171 sequences. (Running on oeis4.)