cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A007279 Number of partitions of n into partition numbers.

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%I A007279 M0558 #54 Jul 02 2025 16:01:55
%S A007279 1,1,2,3,4,6,8,11,14,18,23,29,36,44,54,66,79,95,113,133,157,184,216,
%T A007279 250,290,335,385,442,505,576,656,743,842,951,1070,1204,1351,1514,1691,
%U A007279 1887,2102,2336,2595,2875,3184,3519,3883,4282,4713,5181,5690,6241,6839,7482
%N A007279 Number of partitions of n into partition numbers.
%D A007279 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A007279 Alois P. Heinz, <a href="/A007279/b007279.txt">Table of n, a(n) for n = 0..10000</a>
%H A007279 Igor Pak, <a href="https://arxiv.org/abs/1803.06636">Complexity problems in enumerative combinatorics</a>, arXiv:1803.06636 [math.CO], 2018.
%F A007279 G.f.: 1/Product_{k>=1} (1-q^A000041(k)). - _Michel Marcus_, Jun 20 2018
%p A007279 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 Sellers_, Feb 08 2002
%t A007279 CoefficientList[ Series[1/Product[1 - x^PartitionsP[i], {i, 1, 15}], {x, 0, 50}], x]
%o A007279 (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 A007279 Cf. A000041.
%Y A007279 Cf. A086209, A229362.
%K A007279 nonn
%O A007279 0,3
%A A007279 _N. J. A. Sloane_, _Mira Bernstein_
%E A007279 More terms from _James Sellers_, Feb 08 2002
%E A007279 a(0)=1 prepended by _Alois P. Heinz_, Jul 02 2017