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A370472
G.f. satisfies A(x) = 1 + x * A(x) * (1 - A(x) + A(x)^2 - A(x)^3 + A(x)^4).
6
1, 1, 3, 15, 88, 565, 3844, 27228, 198670, 1482981, 11271117, 86926262, 678568982, 5351340410, 42570335161, 341201704970, 2752693408051, 22335989938093, 182166978172055, 1492496248447713, 12278191839580716, 101382009468089580, 839932374157895727
OFFSET
0,3
FORMULA
G.f. A(x) satisfies:
(1) A(x)^2 = 1 + x * A(x) * (1 + A(x)^5).
(2) A(x) = sqrt(B(x)) where B(x) is the g.f. of A370471.
a(n) = Sum_{k=0..n} binomial(n,k) * binomial(n/2+5*k/2+1/2,n)/(n+5*k+1).
PROG
(PARI) a(n) = sum(k=0, n, binomial(n, k)*binomial(n/2+5*k/2+1/2, n)/(n+5*k+1));
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Mar 31 2024
STATUS
approved