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A365226
G.f. satisfies A(x) = 1 + x*A(x)^5 / (1 + x*A(x)^6).
3
1, 1, 4, 20, 107, 577, 3010, 14429, 56640, 98020, -1297568, -21901213, -232421636, -2081040375, -16862259358, -126674303915, -887771735205, -5768588276072, -33971373570320, -170393703586467, -576946353425125, 1101490168511323, 47657979846612682
OFFSET
0,3
FORMULA
a(n) = Sum_{k=0..n} (-1)^(n-k) * binomial(6*n-k+1,k) * binomial(n-1,n-k)/(6*n-k+1).
PROG
(PARI) a(n) = sum(k=0, n, (-1)^(n-k)*binomial(6*n-k+1, k)*binomial(n-1, n-k)/(6*n-k+1));
CROSSREFS
KEYWORD
sign
AUTHOR
Seiichi Manyama, Aug 27 2023
STATUS
approved