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

1,3

Links

Table of n, a(n) for n=1..22.

Example

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! +...

Prog

(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), ", "))

Crossrefs

Cf. A205804.

Sequence in context: A000608 A333018 A259352 * A329258 A009648 A007125

Adjacent sequences: A205800 A205801 A205802 * A205804 A205805 A205806

Keyword

nonn

Author

Paul D. Hanna, Jan 31 2012

Status

approved