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%I #9 Jun 18 2019 07:32:57
%S 0,2,10,26,90,262,994,3446,13050,48698,185310,705454,2706354,10400626,
%T 40123534,155118406,601106490,2333606254,9075235522,35345263838,
%U 137846899790,538257884918,2104100374694,8233430727646,32247609134418,126410606439062,495918553749434,1946939425794206,7648690681007998,30067266499541098,118264581875657214,465428353255261150
%N Main diagonal of square table A322200.
%H Paul D. Hanna, <a href="/A322201/b322201.txt">Table of n, a(n) for n = 0..400</a>
%F a(n) = coefficient of x^n*y^n/(2*n) in Sum_{n>=1} -log(1 - (x^n + y^n)) for n>=0.
%F a(n) ~ 4^n / sqrt(Pi*n). - _Vaclav Kotesovec_, Jun 18 2019
%e L.g.f.: L(x) = 2*x + 10*x^2/2 + 26*x^3/3 + 90*x^4/4 + 262*x^5/5 + 994*x^6/6 + 3446*x^7/7 + 13050*x^8/8 + 48698*x^9/9 + 185310*x^10/10 + 705454*x^11/11 + 2706354*x^12/12 + ...
%e such that
%e exp( L(x) ) = 1 + 2*x + 7*x^2 + 20*x^3 + 63*x^4 + 190*x^5 + 613*x^6 + 1976*x^7 + 6604*x^8 + 22368*x^9 + 77270*x^10 + 270208*x^11 + 956780*x^12 + ...
%o (PARI)
%o {L = sum(n=1,61, -log(1 - (x^n + y^n) +O(x^61) +O(y^61)) );}
%o {a(n) = polcoeff( 2*n*polcoeff( L,n,x),n,y)}
%o for(n=0,35, print1( a(n),", ") )
%Y Cf. A322200, A322202, A322203, A322205, A322207, A322209.
%K nonn
%O 0,2
%A _Paul D. Hanna_, Nov 30 2018
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