A202144 L.g.f.: (-1/3)*log( Sum_{n>=0} (2*n+1)*(-x)^(n*(n+1)/2) ).

1, 3, 14, 47, 156, 524, 1800, 6159, 20999, 71638, 244608, 835124, 2850836, 9732012, 33223314, 113417951, 387185490, 1321771895, 4512261114, 15403943682, 52585931706, 179517678728, 612836866428, 2092100497612, 7142005837481, 24381356169966, 83232993999782

Offset

1,2

Comments

Compare l.g.f. to: (-1/3)*log( Sum_{n>=0} (-1)^n*(2*n+1)*x^(n*(n+1)/2) ) = Sum_{n>=1} sigma(n)*x^n/n.

Equals one-third the logarithmic derivative of A202143.

Radius of convergence r is approximately equal to:

r = 0.29292898163912377571341042979083759105819894028205070...

where limit a(n)*r^n = 1/3.

Links

Table of n, a(n) for n=1..27.

Example

 L.g.f.: L(x) = x + 3*x^2/2 + 14*x^3/3 + 47*x^4/4 + 156*x^5/5 + 524*x^6/6 +...
where exp(3*L(x)) = 1 + 3*x + 9*x^2 + 32*x^3 + 111*x^4 + 378*x^5 + 1287*x^6 +...+ A202143(n)*x^n +...

Prog

 (PARI) {a(n)=n*polcoeff((-1/3)*log(sum(k=0, sqrtint(2*n+1), (2*k+1)*(-x)^(k*(k+1)/2) +x*O(x^n))), n)}

Crossrefs

Cf. A202143.

Sequence in context: A264501 A104196 A281869 * A287426 A246149 A201349

Adjacent sequences: A202141 A202142 A202143 * A202145 A202146 A202147

Keyword

nonn

Author

Paul D. Hanna, Dec 12 2011

Status

approved