A209335 G.f. A(x) satisfies: A(x) = x / [Sum_{n>=1} (-1)^(n-1) * A(x)^(n*(n-1)/2) * (1 - A(x)^n)/(1 - A(x))].

1, 1, 3, 9, 31, 111, 415, 1591, 6229, 24773, 99793, 406197, 1667803, 6898183, 28710933, 120146889, 505161063, 2132805899, 9037954725, 38424844083, 163843435737, 700477124863, 3001906536983, 12892683275989, 55481600408439, 239188767723227, 1032889415516779

Offset

1,3

Links

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

Example

 G.f.: A(x) = x + x^2 + 3*x^3 + 9*x^4 + 31*x^5 + 111*x^6 + 415*x^7 + 1591*x^8 + 6229*x^9 + 24773*x^10 + 99793*x^11 + 406197*x^12 +...
such that the g.f. satisfies:
x/A(x) = 1 - A(x)*(1-A(x)^2)/(1-A(x)) + A(x)^3*(1-A(x)^3)/(1-A(x)) - A(x)^6*(1-A(x)^4)/(1-A(x)) + A(x)^10*(1-A(x)^5)/(1-A(x)) -+...
Let G(x) satisfy: G(A(x)) = x, then:
G(x) =  x - (x^2 + x^3) + (x^4 + x^5 + x^6) - (x^7 + x^8 + x^9 + x^10) + (x^11 + x^12 + x^13 + x^14 + x^15) +...

Prog

 (PARI) {a(n)=polcoeff(serreverse(x*sum(m=1, n, (-1)^(m-1)*x^(m*(m-1)/2)*(1-x^m)/(1-x)+x*O(x^n))), n)}
for(n=1, 30, print1(a(n), ", "))

Crossrefs

Sequence in context: A120305 A049170 A049174 * A049159 A101473 A056334

Adjacent sequences: A209332 A209333 A209334 * A209336 A209337 A209338

Keyword

nonn

Author

Paul D. Hanna, Mar 06 2012

Status

approved