A279951 Expansion of Product_{k>=1} 1/(1 - x^((k*(k+1)/2)^2)).
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
Offset: 0
Keywords
Examples
a(10) = 2 because we have [9, 1] and [1, 1, 1, 1, 1, 1, 1, 1, 1, 1].
Links
- 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
Programs
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Mathematica
nmax = 105; CoefficientList[Series[Product[1/(1 - x^((k (k + 1)/2)^2)), {k, 1, nmax}], {x, 0, nmax}], x]
Formula
G.f.: Product_{k>=1} 1/(1 - x^((k*(k+1)/2)^2)).
Comments