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A053802 Number of basis partitions of n+49 with Durfee square size 7.

%I A053802 #18 Jul 02 2025 16:01:59
%S A053802 1,2,4,8,14,24,40,64,98,148,218,314,446,622,854,1158,1550,2050,2684,
%T A053802 3478,4464,5682,7172,8982,11170,13796,16928,20648,25040,30198,36234,
%U A053802 43262,51410,60824,71656,84074,98266,114430,132780,153556,177008
%N A053802 Number of basis partitions of n+49 with Durfee square size 7.
%H A053802 Seiichi Manyama, <a href="/A053802/b053802.txt">Table of n, a(n) for n = 0..10000</a>
%H A053802 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.
%H A053802 <a href="/index/Rec#order_28">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,0,0,-1,0,-1,-1,0,1,1,2,0,0,0,-2,-1,-1,0,1,1,0,1,0,0,-1,-1,1).
%F A053802 G.f.: (1+q)(1+q^2)(1+q^3)(1+q^4)(1+q^5)(1+q^6)(1+q^7)/((1-q)(1-q^2)(1-q^3)(1-q^4)(1-q^5)(1-q^6)(1-q^7)).
%F A053802 a(n) = a(n-1) + a(n-2) - a(n-5) - a(n-7) - a(n-8) + a(n-10) + a(n-11) + 2*a(n-12) - 2*a(n-16) - a(n-17) - a(n-18) + a(n-20) + a(n-21) + a(n-23) - a(n-26) - a(n-27) + a(n-28) for n>28. - _Colin Barker_, Jan 02 2020
%t A053802 CoefficientList[Series[Times@@(1+x^Range[7])/Times@@(1-x^Range[7]),{x,0,40}],x] (* _Harvey P. Dale_, Aug 30 2017 *)
%o A053802 (PARI) Vec((1+x)*(1+x^2)*(1+x^3)*(1+x^4)*(1+x^5)*(1+x^6)*(1+x^7) / ((1-x)*(1-x^2)*(1-x^3)*(1-x^4)*(1-x^5)*(1-x^6)*(1-x^7)) + O(x^40)) \\ _Colin Barker_, Jan 02 2020
%K A053802 easy,nonn
%O A053802 0,2
%A A053802 _James Sellers_, Mar 27 2000