A279759 Expansion of Product_{k>=1} 1/(1 - x^(k*(3*k-1)*(3*k-2)/2)).

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9

Offset

0,21

Comments

Number of partitions of n into nonzero dodecahedral numbers (A006566).

Links

Table of n, a(n) for n=0..120.

M. Bernstein and N. J. A. Sloane, Some canonical sequences of integers, Linear Alg. Applications, 226-228 (1995), 57-72; erratum 320 (2000), 210. [Link to arXiv version]

M. Bernstein and N. J. A. Sloane, Some canonical sequences of integers, Linear Alg. Applications, 226-228 (1995), 57-72; erratum 320 (2000), 210. [Link to Lin. Alg. Applic. version together with omitted figures]

OEIS Wiki, Platonic numbers

Index entries for related partition-counting sequences

Formula

G.f.: Product_{k>=1} 1/(1 - x^(k*(3*k-1)*(3*k-2)/2)).

Example

a(21) = 2 because we have [20, 1] and [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1].

Mathematica

nmax=120; CoefficientList[Series[Product[1/(1 - x^(k (3 k - 1) (3 k - 2)/2)), {k, 1, nmax}], {x, 0, nmax}], x]

Crossrefs

Cf. A003108, A006566, A068980, A279757, A279758.

Sequence in context: A037203 A032556 A110592 * A185714 A168353 A053230

Adjacent sequences: A279756 A279757 A279758 * A279760 A279761 A279762

Keyword

nonn

Author

Ilya Gutkovskiy, Dec 18 2016

Status

approved