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A365218
G.f. satisfies A(x) = 1 + x*A(x)^6 / (1 + x*A(x)^6).
3
1, 1, 5, 34, 265, 2232, 19766, 181300, 1706737, 16392049, 159959240, 1581278838, 15800619070, 159321921844, 1618981274136, 16562211506496, 170426473666497, 1762771226922775, 18316562635133813, 191104193378725552, 2001224271292820200
OFFSET
0,3
COMMENTS
Conjecture: Is a(n)>0 correct? It is correct up to the first 10000 terms.
LINKS
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