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A365690
G.f. satisfies A(x) = 1 + x^2*A(x)^4 / (1 - x*A(x)).
3
1, 0, 1, 1, 5, 10, 38, 101, 353, 1070, 3659, 11843, 40505, 135873, 468104, 1604375, 5576315, 19386656, 67950717, 238676813, 842797959, 2983745508, 10603445402, 37777263153, 134985354179, 483438728094, 1735527037388, 6243193190117, 22503637842423
OFFSET
0,5
FORMULA
a(n) = Sum_{k=0..floor(n/2)} binomial(n-k-1,n-2*k) * binomial(n+2*k+1,k) / (n+2*k+1).
PROG
(PARI) a(n) = sum(k=0, n\2, binomial(n-k-1, n-2*k)*binomial(n+2*k+1, k)/(n+2*k+1));
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Sep 16 2023
STATUS
approved