A202143 G.f. 1/[Sum_{n>=0} (2*n+1)*(-x)^(n*(n+1)/2)].

1, 3, 9, 32, 111, 378, 1287, 4395, 15012, 51247, 174930, 597177, 2038676, 6959625, 23758677, 81107291, 276883938, 945225504, 3226807479, 11015664750, 37605240819, 128376648392, 438251781660, 1496102499171, 5107389823160, 17435590684584, 59521562482293

Offset

0,2

Comments

The logarithmic derivative equals 3 times A202144.

Radius of convergence r is approximately equal to:

r = 0.29292898163912377571341042979083759105819894028205070...

where limit a(n)*r^n = 0.81375788478450306387071671675851320912210...

Links

Table of n, a(n) for n=0..26.

Example

 G.f.: A(x) = 1 + 3*x + 9*x^2 + 32*x^3 + 111*x^4 + 378*x^5 + 1287*x^6 +...
where 1/A(x) = 1 - 3*x - 5*x^3 + 7*x^6 + 9*x^10 - 11*x^15 - 13*x^21 + 15*x^28 + 17*x^36 +...+ (2*n+1)*(-x)^(n*(n+1)/2) +...
Compare g.f. A(x) to the cube of the partition function:
P(x)^3 = 1 + 3*x + 9*x^2 + 22*x^3 + 51*x^4 + 108*x^5 + 221*x^6 +...
where 1/P(x)^3 = 1 - 3*x + 5*x^3 - 7*x^6 + 9*x^10 - 11*x^15 + 13*x^21 - 15*x^28 + 17*x^36 +...+ (-1)^n*(2*n+1)*x^(n*(n+1)/2) +...

Prog

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

Crossrefs

Cf. A202144.

Sequence in context: A148975 A148976 A148977 * A330464 A148978 A148979

Adjacent sequences: A202140 A202141 A202142 * A202144 A202145 A202146

Keyword

nonn

Author

Paul D. Hanna, Dec 12 2011

Status

approved