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A371676
G.f. satisfies A(x) = 1 + x * A(x)^2 * (1 + A(x)^(1/2))^2.
3
1, 4, 40, 524, 7824, 126228, 2143544, 37750812, 683194912, 12628104740, 237388091208, 4524456276524, 87228274533040, 1698091537435444, 33332913873239640, 659038408936005692, 13112372856351746112, 262338658739430857796, 5274545338183090647656
OFFSET
0,2
FORMULA
G.f. satisfies A(x) = ( 1 + x * A(x)^2 * (1 + A(x)^(1/2)) )^2.
a(n) = 2 * Sum_{k=0..n} binomial(n,k) * binomial(4*n+k+2,n)/(4*n+k+2).
PROG
(PARI) a(n, r=2, t=4, u=1) = r*sum(k=0, n, binomial(n, k)*binomial(t*n+u*k+r, n)/(t*n+u*k+r));
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Apr 02 2024
STATUS
approved