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A360273
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a(n) = Sum_{k=0..floor(n/2)} Catalan(n-2*k).
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2
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1, 1, 3, 6, 17, 48, 149, 477, 1579, 5339, 18375, 64125, 226387, 807025, 2900827, 10501870, 38258497, 140146660, 515897197, 1907409850, 7080017617, 26373676870, 98562581257, 369433290520, 1388466728581, 5231379691972
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OFFSET
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0,3
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LINKS
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FORMULA
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G.f.: c(x)/(1-x^2), where c(x) is the g.f. of A000108.
D-finite with recurrence (n+1)*a(n) +2*(-2*n+1)*a(n-1) +(-n-1)*a(n-2) +2*(2*n-1)*a(n-3)=0. - R. J. Mathar, Mar 12 2023
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MAPLE
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end proc:
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PROG
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(PARI) a(n) = sum(k=0, n\2, binomial(2*(n-2*k), n-2*k)/(n-2*k+1));
(PARI) my(N=30, x='x+O('x^N)); Vec(2/((1-x^2)*(1+sqrt(1-4*x))))
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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