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 A322207 a(n) = coefficient of x^(3*n)*y^n/n in Sum_{n>=1} -log(1 - (x^n + y^n)). 3

%I #3 Dec 01 2018 10:51:11

%S 1,9,58,473,3881,33786,296017,2630521,23535994,211922929,1917334794,

%T 17417202554,158753389913,1451183583033,13298522310098,

%U 122131739530937,1123787895356429,10358022488568858,95615237915961119,883829035976891713,8179808679273553156,75788358479315971850,702916267465270526873,6525429588311530420858,60629817430084280273281

%N a(n) = coefficient of x^(3*n)*y^n/n in Sum_{n>=1} -log(1 - (x^n + y^n)).

%F a(n) = A322200(3*n,n)/4.

%F Logarithmic derivative of A322208.

%e G.f.: L(x) = x + 9*x^2/2 + 58*x^3/3 + 473*x^4/4 + 3881*x^5/5 + 33786*x^6/6 + 296017*x^7/7 + 2630521*x^8/8 + 23535994*x^9/9 + 211922929*x^10/10 + 1917334794*x^11/11 + 17417202554*x^12/12 + ...

%e such that

%e exp( L(x) ) = 1 + x + 5*x^2 + 24*x^3 + 150*x^4 + 1002*x^5 + 7296*x^6 + 55082*x^7 + 429803*x^8 + 3429141*x^9 + 27861573*x^10 + 229668027*x^11 + 1916090676*x^12 + ... + A322208(n)*x^n + ...

%o (PARI)

%o {L = sum(n=1,121, -log(1 - (x^n + y^n) +O(x^121) +O(y^121)) );}

%o {a(n) = polcoeff( n*polcoeff( L,3*n,x),n,y)}

%o for(n=1,40, print1( a(n),", ") )

%Y Cf. A322200, A322208, A322206, A322204.

%K nonn

%O 1,2

%A _Paul D. Hanna_, Dec 01 2018

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Last modified May 29 04:03 EDT 2023. Contains 363029 sequences. (Running on oeis4.)