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 A322208 G.f.: exp( Sum_{n>=1} A322207(n)*x^n/n ), where A322207(n) is the coefficient of x^(3*n)*y^n/n in Sum_{n>=1} -log(1 - (x^n + y^n)). 1

%I

%S 1,1,5,24,150,1002,7296,55082,429803,3429141,27861573,229668027,

%T 1916090676,16147650896,137259255191,1175441115628,10131538868330,

%U 87826869133114,765203002559216,6697119583569563,58852148074050440,519073825025517314,4593478958169093555,40773010611894321971,362920132925603812683,3238611637275915021439,28968760785263718554360

%N G.f.: exp( Sum_{n>=1} A322207(n)*x^n/n ), where A322207(n) is the coefficient of x^(3*n)*y^n/n in Sum_{n>=1} -log(1 - (x^n + y^n)).

%e G.f.: A(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 + ...

%e such that

%e log( A(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 + ... + A322207(n)*x^n/n + ...

%e RELATED SERIES.

%e A(x)^4 = 1 + 4*x + 26*x^2 + 160*x^3 + 1099*x^4 + 7856*x^5 + 59090*x^6 + 457876*x^7 + 3639573*x^8 + 29479584*x^9 + 242474096*x^10 + ...

%o (PARI)

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

%o {A322207(n) = polcoeff( n*polcoeff( L,3*n,x),n,y)}

%o {a(n) = polcoeff( exp( sum(m=1,n, A322207(m)*x^m/m ) +x*O(x^n) ),n) }

%o for(n=0,40, print1( a(n),", ") )

%Y Cf. A322200, A322207, A322205, A322203.

%K nonn

%O 0,3

%A _Paul D. Hanna_, Dec 01 2018

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Last modified April 2 01:38 EDT 2023. Contains 361723 sequences. (Running on oeis4.)