OFFSET
0,3
COMMENTS
Conjecture: Is a(n)>0 correct? It is correct up to the first 10000 terms.
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..956
FORMULA
a(n) = Sum_{k=0..n} (-1)^k * 2^(n-k) * binomial(n,k) * binomial(6*n+k+1,n)/(6*n+k+1).
a(n) = Sum_{k=0..n} (-2)^(n-k) * binomial(6*n+k+1,k) * binomial(n-1,n-k)/(6*n+k+1).
a(n) = (1/(6*n+1)) * Sum_{k=0..n} (-1)^(n-k) * binomial(6*n+1,k) * binomial(n-1,n-k).
PROG
(PARI) a(n) = sum(k=0, n, (-1)^(n-k)*binomial(6*n+1, k)*binomial(n-1, n-k))/(6*n+1);
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Aug 26 2023
STATUS
approved