OFFSET
1,2
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 1..200
FORMULA
a(n):=1/n*sum(i=1..n, i*sum(k=0..n-i, binomial(k,n-k-i)*3^(k)*(-1)^(n-k+1)*binomial(n+k-1,n-1))).
Recurrence: 7*(n-1)*n*a(n) = (n-1)*(125*n - 252)*a(n-1) - 9*(61*n^2 - 309*n + 388)*a(n-2) - 9*(3*n-8)*(3*n-7)*a(n-3). - Vaclav Kotesovec, Oct 20 2012
a(n) ~ 9^n/(16*Gamma(2/3)*n^(4/3)). - Vaclav Kotesovec, Oct 20 2012
MATHEMATICA
CoefficientList[Series[(1/x) (1- (1 - 9 x)^(1/3)) / (4 - (1 - 9 x)^(1/3)), {x, 0, 20}], x] (* Vaclav Kotesovec, Oct 20 2012 *)
Module[{c=Surd[1-9x, 3]}, Rest[CoefficientList[Series[(1-c)/(4-c), {x, 0, 20}], x]]] (* Harvey P. Dale, Feb 10 2019 *)
PROG
(Maxima)
a(n):=sum(i*sum(binomial(k, n-k-i)*3^(k)*(-1)^(n-k+1)*binomial(n+k-1, n-1), k, 0, n-i), i, 1, n)/n;
CROSSREFS
KEYWORD
nonn
AUTHOR
Vladimir Kruchinin, Dec 20 2011
EXTENSIONS
Typo in Mathematica code fixed by Vincenzo Librandi, Jun 04 2013
STATUS
approved