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

0,2

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.

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

Prog

(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), ", "))

Crossrefs

Column k=9 of A316723.

Sequence in context: A261988 A128770 A280947 * A365667 A069253 A004402

Adjacent sequences: A069249 A069250 A069251 * A069253 A069254 A069255

Keyword

nonn,easy

Author

Benoit Cloitre, Apr 13 2002

Status

approved