|
| |
|
|
A279951
|
|
Expansion of Product_{k>=1} 1/(1 - x^((k*(k+1)/2)^2)).
|
|
0
|
|
|
|
1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 6, 6, 6, 6, 6, 6, 6, 6, 6, 8, 8, 8, 8, 8, 8, 8, 8, 8, 10, 10, 10, 10, 10, 10, 10, 10, 10, 12, 12, 12, 12, 12, 12, 12, 12, 12, 15, 15, 15, 15, 15, 15, 15, 15, 15, 18, 18, 18, 18, 18, 18, 18, 18, 18, 21, 21, 21, 21, 21, 21, 21, 21, 21, 24, 25, 25, 25, 25, 25, 25
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
0,10
|
|
|
COMMENTS
|
Number of partitions of n into nonzero squared triangular numbers (A000537).
|
|
|
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]
Wikipedia, Squared triangular number
Index entries for related partition-counting sequences
|
|
|
FORMULA
|
G.f.: Product_{k>=1} 1/(1 - x^((k*(k+1)/2)^2)).
|
|
|
EXAMPLE
|
a(10) = 2 because we have [9, 1] and [1, 1, 1, 1, 1, 1, 1, 1, 1, 1].
|
|
|
MATHEMATICA
|
nmax = 105; CoefficientList[Series[Product[1/(1 - x^((k (k + 1)/2)^2)), {k, 1, nmax}], {x, 0, nmax}], x]
|
|
|
CROSSREFS
|
Cf. A000537, A007294, A068980.
Sequence in context: A133879 A343609 A054898 * A279224 A167383 A167661
Adjacent sequences: A279948 A279949 A279950 * A279952 A279953 A279954
|
|
|
KEYWORD
|
nonn
|
|
|
AUTHOR
|
Ilya Gutkovskiy, Dec 23 2016
|
|
|
STATUS
|
approved
|
| |
|
|
