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

0,2

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^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

Prog

(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), ", "))

Crossrefs

Column k=10 of A316723.

Sequence in context: A280947 A069252 A365667 * A004402 A015128 A208605

Adjacent sequences: A069250 A069251 A069252 * A069254 A069255 A069256

Keyword

nonn,easy

Author

Benoit Cloitre, Apr 13 2002

Status

approved