login
This site is supported by donations to The OEIS Foundation.

 

Logo

Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing.
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A261049 Expansion of Product_{k>=1} (1+x^k)^(p(k)), where p(k) is the partition function. 21
1, 1, 2, 5, 9, 19, 37, 71, 133, 252, 464, 851, 1547, 2787, 4985, 8862, 15639, 27446, 47909, 83168, 143691, 247109, 423082, 721360, 1225119, 2072762, 3494359, 5870717, 9830702, 16409939, 27309660, 45316753, 74986921, 123748430, 203686778, 334421510, 547735241 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Number of strict multiset partitions of integer partitions of n. Weigh transform of A000041. - Gus Wiseman, Oct 11 2018

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..1000

R. Kaneiwa, An asymptotic formula for Cayley's double partition function p(2; n), Tokyo J. Math. 2, 137-158 (1979).

EXAMPLE

From Gus Wiseman, Oct 11 2018: (Start)

The a(1) = 1 through a(5) = 19 strict multiset partitions:

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

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

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

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

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

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

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

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

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

                                              {{1},{2,2}}

                                              {{2},{1,2}}

                                              {{3},{1,1}}

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

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

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

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

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

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

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

(End)

MAPLE

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

      binomial(combinat[numbpart](i), j)*b(n-i*j, i-1), j=0..n/i)))

    end:

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

seq(a(n), n=0..40);  # Alois P. Heinz, Aug 08 2015

MATHEMATICA

nmax=40; CoefficientList[Series[Product[(1+x^k)^PartitionsP[k], {k, 1, nmax}], {x, 0, nmax}], x]

CROSSREFS

Cf. A000041, A001970, A026007, A027998, A248882, A102866, A256142.

Cf. A047968, A050342, A089259, A305551, A320328, A320330, A320331.

Sequence in context: A014495 A056326 A280247 * A122893 A178841 A214319

Adjacent sequences:  A261046 A261047 A261048 * A261050 A261051 A261052

KEYWORD

nonn

AUTHOR

Vaclav Kotesovec, Aug 08 2015

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 December 7 22:29 EST 2019. Contains 329850 sequences. (Running on oeis4.)