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%I #3 Dec 01 2018 10:22:10
%S 1,7,31,179,1006,6265,38767,245515,1562368,10017042,64512251,
%T 417238925,2707475161,17620153929,114955811686,751616795579,
%U 4923689695592,32308786002880,212327989773919,1397281521970074,9206478467570842,60727722789611357,400978991944396343,2650087221531556021,17529515713716302906,116043807648704288815,768759815833955021344,5096278545391603271517
%N a(n) = coefficient of x^(2*n)*y^n/n in Sum_{n>=1} -log(1 - (x^n + y^n)) for n >= 1.
%F a(n) = A322200(2*n,n)/3.
%e G.f.: L(x) = x + 7*x^2/2 + 31*x^3/3 + 179*x^4/4 + 1006*x^5/5 + 6265*x^6/6 + 38767*x^7/7 + 245515*x^8/8 + 1562368*x^9/9 + 10017042*x^10/10 + 64512251*x^11/11 + 417238925*x^12/12 + ...
%e such that
%e exp( L(x) ) = 1 + x + 4*x^2 + 14*x^3 + 63*x^4 + 294*x^5 + 1526*x^6 + 8157*x^7 + 45332*x^8 + 257378*x^9 + 1489539*x^10 + 8744722*x^11 + 51965701*x^12 + ... + A322206(n)*x^n + ...
%o (PARI)
%o {L = sum(n=1,81, -log(1 - (x^n + y^n) +O(x^81) +O(y^81)) );}
%o {a(n) = polcoeff( n*polcoeff( L,2*n,x),n,y)}
%o for(n=1,35, print1( a(n),", ") )
%Y Cf. A322200, A322206.
%K nonn
%O 1,2
%A _Paul D. Hanna_, Dec 01 2018
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