A205803 E.g.f.: -log( Sum_{n>=0} (-x)^(n*(n+1)/2) / (n*(n+1)/2)! ).

1, 1, 3, 10, 44, 249, 1693, 13384, 120932, 1229759, 13894429, 172677450, 2341111850, 34385290940, 543885462121, 9217332132024, 166621796893824, 3200275345024464, 65082833538054240, 1397097303096855578, 31569176387677926733, 749012642530028865010

Offset: 1

Author

Paul D. Hanna, Jan 31 2012

Keywords

• nonn

Examples

			E.g.f.: A(x) = x + x^2/2! + 3*x^3/3! + 10*x^4/4! + 44*x^5/5! + 249*x^6/6! +...
where
exp(-A(x)) = 1 - x - x^3/3! + x^6/6! + x^10/10! - x^15/15! - x^21/21! +...
		

Crossrefs

Cf. A205804.

Programs

PARI

{a(n) = n!*polcoeff(-log(sum(m=0, sqrtint(2*n+1), (-x)^(m*(m+1)/2)/(m*(m+1)/2)!+x*O(x^n))), n)}
for(n=1,25,print1(a(n),", "))