A322206 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)).

1, 1, 4, 14, 63, 294, 1526, 8157, 45332, 257378, 1489539, 8744722, 51965701, 311915649, 1888382937, 11517313486, 70699038868, 436454255701, 2708000234769, 16877547822830, 105614312726477, 663314865710063, 4179789872458354, 26418030929753007, 167435388627981690, 1063892712455899336, 6775891814778961392, 43249097401730644817, 276606084622479837727, 1772391802339441687335, 11376702892986621823617

Offset: 0

Author

Paul D. Hanna, Dec 01 2018

Keywords

• nonn

Examples

			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 + ...
such that
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 + ...
RELATED SERIES.
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 + ...
		

Crossrefs

Cf. A322200, A322205, A322204.

Programs

PARI

{L = sum(n=1,81, -log(1 - (x^n + y^n) +O(x^81) +O(y^81)) );}
{A322205(n) = polcoeff( n*polcoeff( L,2*n,x),n,y)}
{a(n) = polcoeff( exp( sum(m=1,n, A322205(m)*x^m/m ) +x*O(x^n) ),n) }
for(n=0,40, print1( a(n),", ") )