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A365798
G.f. satisfies A(x) = 1 + x*A(x)*(1 + x^5*A(x)^4).
0
1, 1, 1, 1, 1, 1, 2, 7, 22, 57, 127, 253, 468, 848, 1618, 3433, 8009, 19384, 46264, 106369, 235179, 505955, 1079790, 2332555, 5166405, 11737860, 27086236, 62676956, 144074416, 327837356, 739787486, 1663922487, 3751649542, 8513640107, 19464624667
OFFSET
0,7
FORMULA
a(n) = Sum_{k=0..floor(n/6)} binomial(n-5*k,k) * binomial(n-k+1,n-5*k) / (n-k+1) = Sum_{k=0..floor(n/6)} binomial(n-k,5*k) * binomial(5*k,k) / (4*k+1).
PROG
(PARI) a(n) = sum(k=0, n\6, binomial(n-5*k, k)*binomial(n-k+1, n-5*k)/(n-k+1));
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Sep 19 2023
STATUS
approved