A216317 G.f.: 1/( (1-8*x)*(1+x)^2 )^(1/6).

1, 1, 6, 34, 217, 1449, 9996, 70512, 505674, 3672682, 26943748, 199284540, 1483955746, 11113108930, 83628685440, 631963708200, 4793067536265, 36469419494985, 278278625232510, 2128794954411930, 16322188021280505, 125405739232800585, 965313101906567700

Offset

0,3

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Formula

G.f.: exp( Sum_{n>=1} A007613(n)/2 * x^n/n ) where A007613(n) = Sum_{k=0..n} binomial(3*n,3*k).

Recurrence: n*a(n) = (7*n-6)*a(n-1) + 4*(2*n-3)*a(n-2). - Vaclav Kotesovec, Oct 20 2012

a(n) ~ Gamma(5/6)*8^n/(3^(2/3)*Pi*n^(5/6)). - Vaclav Kotesovec, Oct 20 2012

Example

G.f.: A(x) = 1 + x + 6*x^2 + 34*x^3 + 217*x^4 + 1449*x^5 + 9996*x^6 +...
where 1/A(x)^6 = 1 - 6*x - 15*x^2 - 8*x^3.
The logarithm of the g.f. begins:
log(A(x)) = x + 11*x^2/2 + 85*x^3/3 + 683*x^4/4 + 5461*x^5/5 + 43691*x^6/6 +...+ A007613(n)/2*x^n/n +...

Mathematica

CoefficientList[Series[1/((1-8*x)*(1+x)^2)^(1/6), {x, 0, 20}], x] (* Vaclav Kotesovec, Oct 20 2012 *)

Prog

(PARI) {a(n)=polcoeff(1/( (1-8*x)*(1+x)^2 +x*O(x^n) )^(1/6), n)}
(PARI) {a(n)=local(A=1+x); A=exp(sum(m=1, n+1, sum(j=0, m, binomial(3*m, 3*j))/2*x^m/m +x*O(x^n))); polcoeff(A, n)}
for(n=0, 31, print1(a(n), ", "))

Crossrefs

Cf. A216316, A007613.

Sequence in context: A266431 A063090 A184185 * A370324 A230331 A267242

Adjacent sequences: A216314 A216315 A216316 * A216318 A216319 A216320

Keyword

nonn

Author

Paul D. Hanna, Sep 03 2012

Status

approved