A069251 Number of basis partitions of n+64 with Durfee square size 8.

1, 2, 4, 8, 14, 24, 40, 64, 100, 152, 226, 330, 474, 670, 934, 1286, 1748, 2350, 3128, 4122, 5384, 6974, 8960, 11426, 14468, 18196, 22740, 28248, 34888, 42854, 52366, 63670, 77048, 92816, 111324, 132970, 158194, 187482, 221380, 260488, 305466

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^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^8 +1)/((x -1)^8*(x^2 +x +1)^2*(x^4 +x^3 +x^2 +x +1)*(x^6 +x^5 +x^4 +x^3 +x^2 +x +1)). [Colin Barker, Sep 23 2012]

Prog

(PARI) s=8; 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=8 of A316723.

Sequence in context: A091779 A365666 A090399 * A261988 A128770 A280947

Adjacent sequences: A069248 A069249 A069250 * A069252 A069253 A069254

Keyword

nonn,easy

Author

Benoit Cloitre, Apr 13 2002

Status

approved