A069253 Number of basis partitions of n+100 with Durfee square size 10.

1, 2, 4, 8, 14, 24, 40, 64, 100, 154, 232, 342, 498, 714, 1010, 1414, 1956, 2678, 3634, 4886, 6514, 8618, 11316, 14754, 19112, 24600, 31472, 40038, 50656, 63754, 79844, 99514, 123460, 152500, 187572, 229770, 280364, 340806, 412768, 498176, 599216

Offset: 0

Author

Benoit Cloitre, Apr 13 2002

Keywords

• nonn
• easy
• changed

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=10 of A316723.

Programs

PARI

s=10; 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^2 -x +1) * (x^2 +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 -x^6 +x^4 -x^2 +1) * (x^8 +1) / ((x -1)^10 * (x^2 +x +1)^3 * (x^4 +x^3 +x^2 +x +1)^2 * (x^6 +x^3 +1) * (x^6 +x^5 +x^4+ x^3 +x^2 +x +1)). - Colin Barker, Jul 13 2013