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A280253
Expansion of Product_{k>=1} (1 + x^p(k)), where p(k) is the number of partitions of k (A000041).
4
1, 1, 1, 2, 1, 2, 2, 2, 3, 2, 3, 3, 3, 3, 3, 4, 4, 4, 5, 4, 4, 5, 5, 6, 5, 6, 6, 6, 6, 6, 7, 6, 7, 8, 7, 7, 8, 8, 9, 8, 9, 9, 9, 10, 9, 11, 9, 10, 12, 10, 11, 11, 11, 12, 11, 12, 13, 13, 14, 14, 14, 13, 13, 15, 15, 14, 15, 15, 15, 15, 15, 16, 16, 16, 17, 17, 15, 17, 19, 19, 20, 19, 20, 20, 19, 21, 20, 20, 21, 21, 22
OFFSET
0,4
COMMENTS
Number of partitions of n into distinct partition numbers.
LINKS
M. Bernstein and N. J. A. Sloane, Some canonical sequences of integers, Linear Alg. Applications, 226-228 (1995), 57-72; erratum 320 (2000), 210. [Link to arXiv version]
M. Bernstein and N. J. A. Sloane, Some canonical sequences of integers, Linear Alg. Applications, 226-228 (1995), 57-72; erratum 320 (2000), 210. [Link to Lin. Alg. Applic. version together with omitted figures]
Eric Weisstein's World of Mathematics, Partition Function P, Partition Function Q
FORMULA
G.f.: Product_{k>=1} (1 + x^p(k)).
EXAMPLE
a(8) = 3 because we have [7, 1], [5, 3] and [5, 2, 1].
MATHEMATICA
nmax = 90; CoefficientList[Series[Product[(1 + x^PartitionsP[k]), {k, 1, nmax}], {x, 0, nmax}], x]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Dec 30 2016
STATUS
approved