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A371607
G.f. satisfies A(x) = ( 1 + x * (1 + x*A(x)^2) )^2.
1
1, 2, 3, 10, 29, 92, 314, 1078, 3830, 13844, 50746, 188554, 707667, 2679960, 10227940, 39294772, 151859858, 589943516, 2302462140, 9023681820, 35498194465, 140122652960, 554827907272, 2203135245820, 8771143399104, 35003747271444, 140002994665366
OFFSET
0,2
FORMULA
a(n) = Sum_{k=0..n} binomial(4*(n-k)+2,k) * binomial(k,n-k)/(2*(n-k)+1).
G.f.: A(x) = B(x)^2 where B(x) is the g.f. of A137954.
PROG
(PARI) a(n, r=2, s=1, t=0, u=4) = 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
Sequence in context: A084380 A363139 A286814 * A338583 A121909 A153909
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Mar 29 2024
STATUS
approved