A279758 Expansion of Product_{k>=1} 1/(1 - x^(k*(5*k^2-5*k+2)/2)).

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15

Offset

0,13

Comments

Number of partitions of n into nonzero icosahedral numbers (A006564).

Links

Table of n, a(n) for n=0..105.

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*(5*k^2-5*k+2)/2)).

Example

a(13) = 2 because we have [12, 1] and [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1].

Mathematica

nmax=105; CoefficientList[Series[Product[1/(1 - x^(k (5 k^2 - 5 k + 2)/2)), {k, 1, nmax}], {x, 0, nmax}], x]

Crossrefs

Cf. A003108, A006564, A068980, A279757, A279759.

Sequence in context: A071701 A342696 A064459 * A082996 A094382 A146167

Adjacent sequences: A279755 A279756 A279757 * A279759 A279760 A279761

Keyword

nonn

Author

Ilya Gutkovskiy, Dec 18 2016

Status

approved