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%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
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