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 A322203 a(n) = coefficient of x^n*y^n/n in Sum_{n>=1} -log(1 - (x^n + y^n)), for n >= 1. 7

%I

%S 1,5,13,45,131,497,1723,6525,24349,92655,352727,1353177,5200313,

%T 20061767,77559203,300553245,1166803127,4537617761,17672631919,

%U 68923449895,269128942459,1052050187347,4116715363823,16123804567209,63205303219531,247959276874717,973469712897103,3824345340503999,15033633249770549,59132290937828607,232714176627630575,916312071072401757

%N a(n) = coefficient of x^n*y^n/n in Sum_{n>=1} -log(1 - (x^n + y^n)), for n >= 1.

%H Paul D. Hanna, <a href="/A322203/b322203.txt">Table of n, a(n) for n = 1..400</a>

%F a(n) = A322200(n,n)/2 for n >= 1.

%F a(n) ~ 2^(2*n-1) / sqrt(Pi*n). - _Vaclav Kotesovec_, Jun 18 2019

%e G.f.: L(x) = x + 5*x^2/2 + 13*x^3/3 + 45*x^4/4 + 131*x^5/5 + 497*x^6/6 + 1723*x^7/7 + 6525*x^8/8 + 24349*x^9/9 + 92655*x^10/10 + 352727*x^11/11 + 1353177*x^12/12 + ...

%e such that

%e exp( L(x) ) = 1 + x + 3*x^2 + 7*x^3 + 20*x^4 + 54*x^5 + 168*x^6 + 518*x^7 + 1702*x^8 + 5672*x^9 + 19413*x^10 + 67329*x^11 + ... + A322204(n)*x^n + ...

%o (PARI)

%o {L = sum(n=1,61, -log(1 - (x^n + y^n) +O(x^61) +O(y^61)) );}

%o {a(n) = polcoeff( n*polcoeff( L,n,x),n,y)}

%o for(n=1,35, print1( a(n),", ") )

%Y Cf. A322204, A322202, A322200.

%K nonn

%O 1,2

%A _Paul D. Hanna_, Nov 30 2018

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Last modified April 11 14:58 EDT 2021. Contains 342886 sequences. (Running on oeis4.)