OFFSET
1,2
LINKS
Paul D. Hanna, Table of n, a(n) for n = 1..100
FORMULA
a(n) = A274713(n) / (n*(n+1)/2), where A274713(n) is the number of partitions of a {3*n-1}-set into n nonempty subsets.
a(n) = 1/n! * Sum_{k=1..n} (-1)^(n-k) * binomial(n,k) * k^(3*n-1) / (n*(n+1)/2).
a(n) ~ sqrt(2) * 3^(3*n-1) * n^(2*n-7/2) / (exp(2*n) * c^n * (3-c)^(2*n-1) * sqrt(Pi*(1-c))), where c = -LambertW(-3*exp(-3)) = 0.1785606278779211... = -A226750. - Vaclav Kotesovec, Jul 06 2016
PROG
(PARI) {a(n) = polcoeff( 1/prod(k=1, n, 1-k*x +x*O(x^(2*n))), 2*n-1) / (n*(n+1)/2)}
for(n=1, 20, print1(a(n), ", "))
(PARI) {a(n) = abs( stirling(3*n-1, n, 2) / (n*(n+1)/2) )}
for(n=1, 20, print1(a(n), ", "))
(PARI) {a(n) = 1/n! * sum(k=0, n, (-1)^(n-k) * binomial(n, k) * k^(3*n-1)) / (n*(n+1)/2)}
for(n=1, 20, print1(a(n), ", "))
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Jul 03 2016
STATUS
approved