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, 1, 5, 24, 150, 1002, 7296, 55082, 429803, 3429141, 27861573, 229668027, 1916090676, 16147650896, 137259255191, 1175441115628, 10131538868330, 87826869133114, 765203002559216, 6697119583569563, 58852148074050440, 519073825025517314, 4593478958169093555, 40773010611894321971, 362920132925603812683, 3238611637275915021439, 28968760785263718554360

Offset: 0

Author

Paul D. Hanna, Dec 01 2018

Keywords

• nonn

Examples

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

Crossrefs

Cf. A322200, A322207, A322205, A322203.

Programs

PARI

{L = sum(n=1,121, -log(1 - (x^n + y^n) +O(x^121) +O(y^121)) );}
{A322207(n) = polcoeff( n*polcoeff( L,3*n,x),n,y)}
{a(n) = polcoeff( exp( sum(m=1,n, A322207(m)*x^m/m ) +x*O(x^n) ),n) }
for(n=0,40, print1( a(n),", ") )