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=== Generating function ===
The generating function for the numbers ''q''(''n'') is given by a simple infinite product:<ref>{{cite book|first=Richard P.|last=Stanley|author-link=Richard P. Stanley|title=Enumerative Combinatorics 1 |series=Cambridge Studies in Advanced Mathematics|volume=49|publisher=Cambridge University Press|isbn=0-521-66351-2 |year=1997|at=Proof of Proposition 1.8.5}}</ref>
<math display="block">\sum_{n=0}^{\infty} q(n)x^n = \prod_{k = 1}^\infty (1 + x^
where the notation <math>(a;b)_{\infty}</math> represents the [[Pochhammer symbol]] <math>(a;b)_{\infty} = \prod_{k = 0}^{\infty} (1 - ab^{k}).</math> From this formula, one may easily obtain the first few terms {{OEIS|A000009}}:
<math display="block">\sum_{n=0}^{\infty} q(n)x^n = 1+1x+1x^2+2x^3+2x^4+3x^5+4x^6+5x^7+6x^8+8x^9+10x^{10}+\ldots.</math>
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