A322203 a(n) = coefficient of x^n*y^n/n in Sum_{n>=1} -log(1 - (x^n + y^n)), for n >= 1.

1, 5, 13, 45, 131, 497, 1723, 6525, 24349, 92655, 352727, 1353177, 5200313, 20061767, 77559203, 300553245, 1166803127, 4537617761, 17672631919, 68923449895, 269128942459, 1052050187347, 4116715363823, 16123804567209, 63205303219531, 247959276874717, 973469712897103, 3824345340503999, 15033633249770549, 59132290937828607, 232714176627630575, 916312071072401757

Offset: 1

Author

Paul D. Hanna, Nov 30 2018

Keywords

• nonn

Examples

			G.f.: L(x) = x + 5*x^2/2 + 13*x^3/3 + 45*x^4/4 + 131*x^5/5 + 497*x^6/6 + 1723*x^7/7 + 6525*x^8/8 + 24349*x^9/9 + 92655*x^10/10 + 352727*x^11/11 + 1353177*x^12/12 + ...
such that
exp( L(x) ) = 1 + x + 3*x^2 + 7*x^3 + 20*x^4 + 54*x^5 + 168*x^6 + 518*x^7 + 1702*x^8 + 5672*x^9 + 19413*x^10 + 67329*x^11 + ... + A322204(n)*x^n + ...
		

Links

• Paul D. Hanna, Table of n, a(n) for n = 1..400

Crossrefs

Cf. A322204, A322202, A322200.

Programs

PARI

{L = sum(n=1,61, -log(1 - (x^n + y^n) +O(x^61) +O(y^61)) );}
{a(n) = polcoeff( n*polcoeff( L,n,x),n,y)}
for(n=1,35, print1( a(n),", ") )

Formula

a(n) = A322200(n,n)/2 for n >= 1.

a(n) ~ 2^(2*n-1) / sqrt(Pi*n). - Vaclav Kotesovec, Jun 18 2019