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A369618
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Expansion of (1/x) * Series_Reversion( x / (1/(1-x) + x^2) ).
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2
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1, 1, 3, 8, 26, 87, 308, 1122, 4196, 15995, 61953, 243091, 964307, 3860820, 15581231, 63318119, 258874412, 1064093055, 4394851631, 18229191263, 75904152261, 317161817092, 1329465389854, 5589012748902, 23558679647629, 99548061405442, 421598837336178
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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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a(n) = (1/(n+1)) * Sum_{k=0..floor(n/2)} binomial(n+1,k) * binomial(2*n-3*k,n-2*k).
D-finite with recurrence +(n+2)*(n+1)*a(n) -(n+1)*(13*n-4)*a(n-1) +2*(26*n^2-36*n+1)*a(n-2) +(-61*n^2+219*n-176)*a(n-3) +2*(-26*n^2+78*n-7)*a(n-4) +(235*n-497)*(n-4)*a(n-5) -93*(n-4)*(n-5)*a(n-6)=0. - R. J. Mathar, Jan 28 2024
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PROG
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(PARI) my(N=30, x='x+O('x^N)); Vec(serreverse(x/(1/(1-x)+x^2))/x)
(PARI) a(n) = sum(k=0, n\2, binomial(n+1, k)*binomial(2*n-3*k, n-2*k))/(n+1);
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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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