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 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

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