A007279 Number of partitions of n into partition numbers. (Formerly M0558)

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

0,3

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.

Formula

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

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 A. Sellers, Feb 08 2002

Mathematica

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

Prog

(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

Crossrefs

Cf. A000041.

Cf. A086209, A229362.

Sequence in context: A175870 A114829 A175869 * A034891 A143611 A279075

Adjacent sequences: A007276 A007277 A007278 * A007280 A007281 A007282

Keyword

nonn

Author

N. J. A. Sloane, Mira Bernstein

Extensions

More terms from James A. Sellers, Feb 08 2002

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

Status

approved