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%I #13 Jun 26 2016 10:45:51
%S 1,1,5,23,101,377,1226,3507,9027,21224,46262,94512,182702,336666,
%T 595085,1014091,1673243,2682685,4192118,6401314,9572962,14047457,
%U 20260601,28763703,40247228,55567352,75776769,102158957,136267461,179969238,235493851,305487369
%N Number of partitions of n^2 into at most five parts.
%H Colin Barker, <a href="/A274322/b274322.txt">Table of n, a(n) for n = 0..1000</a>
%F Coefficient of x^(n^2) in 1/((1-x)*(1-x^2)*(1-x^3)*(1-x^4)*(1-x^5)).
%F a(n) = A001401(n^2).
%F Empirical g.f.: (1 -3*x +4*x^2 +13*x^3 +21*x^4 +63*x^5 +138*x^6 +204*x^7 +257*x^8 +280*x^9 +267*x^10 +201*x^11 +128*x^12 +67*x^13 +31*x^14 +6*x^15 +x^16 +x^17) / ((1 -x)^9*(1 +x)^3*(1 +x +x^2)*(1 +x +x^2 +x^3 +x^4)).
%o (PARI)
%o \\ b(n) is the coefficient of x^n in the g.f. 1/((1-x)*(1-x^2)*(1-x^3)*(1-x^4)*(1-x^5)).
%o b(n) = round(((n+5)^4+10*((n+5)^3+(n+5)^2)-75*(n+5)-45*(n+5)*(-1)^(n+5))/2880)
%o vector(40, n, n--; b(n^2))
%Y A subsequence of A001401.
%K nonn
%O 0,3
%A _Colin Barker_, Jun 20 2016
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