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A259335
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a(n) = ( Sum_{k=0..n} binomial(2*n, k)^2 * (binomial(2*n, k+1) - binomial(2*n, k-1)) )/(n*binomial(2*n, n)).
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2
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1, 7, 61, 611, 6686, 77729, 944245, 11859355, 152893720, 2013070126, 26967817306, 366542344117, 5043651762826, 70138959074461, 984384594022117, 13927418363218955, 198459156018467084, 2845950809029225472, 41044332341739034032, 594983281327999736694
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OFFSET
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1,2
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LINKS
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H. W. Gould, Problem E2384, Amer. Math. Monthly, 79 (1972), p. 1034.
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FORMULA
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a(n) = (1/(n+1)) * Sum_{k=0..n} (k/(n+k)) * binomial(n+k,k)^2. - Seiichi Manyama, Jul 16 2024
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MAPLE
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f:=proc(n) local b;
b:=binomial;
add(b(2*n, k)^2*(b(2*n, k+1)-b(2*n, k-1)), k=0..n)/(n*b(2*n, n));
end;
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PROG
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(PARI) a(n) = sum(k=0, n, k/(n+k)*binomial(n+k, k)^2)/(n+1); \\ Seiichi Manyama, Jul 16 2024
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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