A280253 Expansion of Product_{k>=1} (1 + x^p(k)), where p(k) is the number of partitions of k (A000041).

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

Alois P. Heinz, Table of n, a(n) for n = 0..20000

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

Index entries for related partition-counting sequences

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

Cf. A000009, A000041, A007279, A086209.

Sequence in context: A218469 A343333 A230502 * A008677 A036497 A211976

Adjacent sequences: A280250 A280251 A280252 * A280254 A280255 A280256

Keyword

nonn

Author

Ilya Gutkovskiy, Dec 30 2016

Status

approved