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

1, 9, 58, 473, 3881, 33786, 296017, 2630521, 23535994, 211922929, 1917334794, 17417202554, 158753389913, 1451183583033, 13298522310098, 122131739530937, 1123787895356429, 10358022488568858, 95615237915961119, 883829035976891713, 8179808679273553156, 75788358479315971850, 702916267465270526873, 6525429588311530420858, 60629817430084280273281

Offset: 1

Author

Paul D. Hanna, Dec 01 2018

Keywords

• nonn

Examples

			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 + ...
such that
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 + ...
		

Crossrefs

Cf. A322200, A322208, A322206, A322204.

Programs

PARI

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

Formula

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

Logarithmic derivative of A322208.