

A279758


Expansion of Product_{k>=1} 1/(1  x^(k*(5*k^25*k+2)/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
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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, 226228 (1995), 5772; erratum 320 (2000), 210. [Link to arXiv version]
M. Bernstein and N. J. A. Sloane, Some canonical sequences of integers, Linear Alg. Applications, 226228 (1995), 5772; erratum 320 (2000), 210. [Link to Lin. Alg. Applic. version together with omitted figures]
OEIS Wiki, Platonic numbers
Index entries for related partitioncounting sequences


FORMULA

G.f.: Product_{k>=1} 1/(1  x^(k*(5*k^25*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: A111855 A071701 A064459 * A082996 A094382 A146167
Adjacent sequences: A279755 A279756 A279757 * A279759 A279760 A279761


KEYWORD

nonn


AUTHOR

Ilya Gutkovskiy, Dec 18 2016


STATUS

approved



