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A365731
G.f. satisfies A(x) = 1 + x^4*A(x)^5*(1 + x*A(x)).
5
1, 0, 0, 0, 1, 1, 0, 0, 5, 11, 6, 0, 35, 120, 136, 51, 285, 1330, 2310, 1771, 3036, 14950, 35100, 40950, 47502, 175392, 503440, 791120, 927520, 2272424, 7037184, 13803405, 18643560, 33997080, 98920536, 226318196, 359255325, 578590155, 1445166360, 3584815443, 6573439928
OFFSET
0,9
FORMULA
a(n) = Sum_{k=0..floor(n/4)} binomial(k,n-4*k) * binomial(n+k+1,k) / (n+k+1).
G.f.: (1/x) * Series_Reversion( x*(1 - x^4*(1 + x)) ). - _ Seiichi Manyama_, Sep 24 2024
PROG
(PARI) a(n) = sum(k=0, n\4, binomial(k, n-4*k)*binomial(n+k+1, k)/(n+k+1));
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Sep 17 2023
STATUS
approved