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Number of partitions of n into partition numbers.
(Formerly M0558)
13

%I M0558 #53 Jun 23 2018 03:11:21

%S 1,1,2,3,4,6,8,11,14,18,23,29,36,44,54,66,79,95,113,133,157,184,216,

%T 250,290,335,385,442,505,576,656,743,842,951,1070,1204,1351,1514,1691,

%U 1887,2102,2336,2595,2875,3184,3519,3883,4282,4713,5181,5690,6241,6839,7482

%N Number of partitions of n into partition numbers.

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H Alois P. Heinz, <a href="/A007279/b007279.txt">Table of n, a(n) for n = 0..10000</a>

%H Igor Pak, <a href="https://arxiv.org/abs/1803.06636">Complexity problems in enumerative combinatorics</a>, arXiv:1803.06636 [math.CO], 2018.

%F G.f.: 1/Product_{k>=1} (1-q^A000041(k)). - _Michel Marcus_, Jun 20 2018

%p with(combinat): gf := 1/product((1-q^numbpart(k)), k=1..20): s := series(gf, q, 200): for i from 0 to 199 do printf(`%d,`,coeff(s, q, i)) od: # _James A. Sellers_, Feb 08 2002

%t CoefficientList[ Series[1/Product[1 - x^PartitionsP[i], {i, 1, 15}], {x, 0, 50}], x]

%o (PARI) seq(n)={my(t=1); while(numbpart(t+1)<=n, t++); Vec(1/prod(k=1, t, 1-x^numbpart(k) + O(x*x^n)))} \\ _Andrew Howroyd_, Jun 22 2018

%Y Cf. A000041.

%Y Cf. A086209, A229362.

%K nonn

%O 0,3

%A _N. J. A. Sloane_, _Mira Bernstein_

%E More terms from _James A. Sellers_, Feb 08 2002

%E a(0)=1 prepended by _Alois P. Heinz_, Jul 02 2017