A322206 - OEIS

%I #7 Dec 01 2018 10:26:05

%S 1,1,4,14,63,294,1526,8157,45332,257378,1489539,8744722,51965701,

%T 311915649,1888382937,11517313486,70699038868,436454255701,

%U 2708000234769,16877547822830,105614312726477,663314865710063,4179789872458354,26418030929753007,167435388627981690,1063892712455899336,6775891814778961392,43249097401730644817,276606084622479837727,1772391802339441687335,11376702892986621823617

%N G.f.: exp( Sum_{n>=1} A322205(n)*x^n/n ), where A322205(n) is the coefficient of x^(2*n)*y^n/n in Sum_{n>=1} -log(1 - (x^n + y^n)).

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

%e such that

%e log( A(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 + ... + A322205(n)*x^n/n + ...

%e RELATED SERIES.

%e A(x)^3 = 1 + 3*x + 15*x^2 + 67*x^3 + 333*x^4 + 1686*x^5 + 9031*x^6 + 49629*x^7 + 280467*x^8 + 1614932*x^9 + 9449961*x^10 + 56001366*x^11 + 335437797*x^12 + ...

%o (PARI)

%o {L = sum(n=1,81, -log(1 - (x^n + y^n) +O(x^81) +O(y^81)) );}

%o {A322205(n) = polcoeff( n*polcoeff( L,2*n,x),n,y)}

%o {a(n) = polcoeff( exp( sum(m=1,n, A322205(m)*x^m/m ) +x*O(x^n) ),n) }

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

%Y Cf. A322200, A322205, A322204.

%K nonn

%O 0,3

%A _Paul D. Hanna_, Dec 01 2018