A007279 Number of partitions of n into partition numbers.

1, 1, 2, 3, 4, 6, 8, 11, 14, 18, 23, 29, 36, 44, 54, 66, 79, 95, 113, 133, 157, 184, 216, 250, 290, 335, 385, 442, 505, 576, 656, 743, 842, 951, 1070, 1204, 1351, 1514, 1691, 1887, 2102, 2336, 2595, 2875, 3184, 3519, 3883, 4282, 4713, 5181, 5690, 6241, 6839, 7482

Offset: 0

Author

N. J. A. Sloane, Mira Bernstein

Keywords

• nonn

References

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

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..10000
• Igor Pak, Complexity problems in enumerative combinatorics, arXiv:1803.06636 [math.CO], 2018.

Crossrefs

Cf. A000041.

Cf. A086209, A229362.

Programs

Maple

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

Mathematica

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

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

Formula

G.f.: 1/Product_{k>=1} (1-q^A000041(k)). - Michel Marcus, Jun 20 2018

Extensions

More terms from James Sellers, Feb 08 2002

a(0)=1 prepended by Alois P. Heinz, Jul 02 2017