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A069253
Number of basis partitions of n+100 with Durfee square size 10.
2
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
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
KEYWORD
nonn,easy
AUTHOR
Benoit Cloitre, Apr 13 2002
STATUS
approved