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A371577
G.f. satisfies A(x) = ( 1 + x*A(x)^2 * (1 + x) )^2.
2
1, 2, 11, 70, 505, 3910, 31772, 267280, 2307982, 20339946, 182207333, 1654250474, 15187764411, 140767293560, 1315349040350, 12377806027892, 117200381305538, 1115791797318548, 10674418686087377, 102563189093302366, 989321056200478417
OFFSET
0,2
FORMULA
a(n) = Sum_{k=0..n} binomial(4*k+2,k) * binomial(k,n-k)/(2*k+1).
G.f.: A(x) = B(x)^2 where B(x) is the g.f. of A365178.
PROG
(PARI) a(n, r=2, s=1, t=4, u=0) = r*sum(k=0, n, binomial(t*k+u*(n-k)+r, k)*binomial(s*k, n-k)/(t*k+u*(n-k)+r));
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Mar 28 2024
STATUS
approved