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Number of basis partitions of n+100 with Durfee square size 10.
2

%I #19 Jul 18 2018 02:30:09

%S 1,2,4,8,14,24,40,64,100,154,232,342,498,714,1010,1414,1956,2678,3634,

%T 4886,6514,8618,11316,14754,19112,24600,31472,40038,50656,63754,79844,

%U 99514,123460,152500,187572,229770,280364,340806,412768,498176,599216

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

%H Seiichi Manyama, <a href="/A069253/b069253.txt">Table of n, a(n) for n = 0..10000</a>

%H M. D. Hirschhorn, <a href="https://doi.org/10.1016/S0012-365X(99)00030-8">Basis partitions and Rogers-Ramanujan partitions</a>, Discrete Math. 205 (1999), 241-243.

%F 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

%o (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),","))

%Y Column k=10 of A316723.

%K nonn,easy

%O 0,2

%A _Benoit Cloitre_, Apr 13 2002