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A365189
G.f. satisfies A(x) = 1 + x*A(x)^5*(1 + x*A(x)^5).
9
1, 1, 6, 50, 485, 5130, 57391, 667777, 7999095, 97986680, 1221813880, 15456556791, 197887386913, 2559189842240, 33383097891135, 438714241508615, 5803049210371375, 77199163872173757, 1032215519193531310, 13864180990526161995, 186975433988014039830
OFFSET
0,3
LINKS
Jun Yan, Lattice paths enumerations weighted by ascent lengths, arXiv:2501.01152 [math.CO], 2025. See p. 13.
FORMULA
a(n) = (1/(5*n+1)) * Sum_{k=0..floor(n/2)} binomial(n-k,k) * binomial(5*n+1,n-k).
PROG
(PARI) a(n) = sum(k=0, n\2, binomial(n-k, k)*binomial(5*n+1, n-k))/(5*n+1);
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Aug 25 2023
STATUS
approved