A069252 Number of basis partitions of n+81 with Durfee square size 9.

1, 2, 4, 8, 14, 24, 40, 64, 100, 154, 230, 338, 490, 698, 982, 1366, 1876, 2550, 3434, 4578, 6052, 7938, 10328, 13342, 17120, 21820, 27640, 34810, 43588, 54290, 67278, 82958, 101816, 124404, 151340, 183350, 221252, 265958, 318524, 380132, 452094

Offset: 0

Author

Benoit Cloitre, Apr 13 2002

Keywords

• nonn
• easy

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..10000
• M. D. Hirschhorn, Basis partitions and Rogers-Ramanujan partitions, Discrete Math. 205 (1999), 241-243.

Crossrefs

Column k=9 of A316723.

Programs

PARI

s=9; a(n)=polcoeff(prod(i=1,s,(1+x^i))/(prod(i=1,s,(1-x^i))+x*O(x^n)),n) for(n=0,50,print1(a(n),","))

Formula

G.f.: -(x +1) * (x^2 -x +1) * (x^4 -x^3 +x^2 -x +1) * (x^4 -x^2 +1) * (x^6 -x^5 +x^4 -x^3 +x^2 -x +1) * (x^6 -x^3 +1) * (x^8 +1) / ((x -1)^9 * (x^2 +x +1)^3 * (x^4 +x^3 +x^2 +x +1) * (x^6 +x^3 +1) * (x^6 +x^5 +x^4 +x^3 +x^2 +x +1)). - Colin Barker, Jul 13 2013