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A370196
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Coefficient of x^n in the expansion of ( (1+x)^2 * (1+x^3) )^n.
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1
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1, 2, 6, 23, 102, 477, 2259, 10733, 51174, 245156, 1180381, 5709387, 27723315, 135055845, 659744973, 3230479173, 15850993126, 77918426928, 383646423564, 1891715752242, 9340099603677, 46170434726054, 228479085858447, 1131770152854441, 5611302030239667
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OFFSET
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0,2
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LINKS
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FORMULA
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a(n) = Sum_{k=0..floor(n/3)} binomial(n,k) * binomial(2*n,n-3*k).
The g.f. exp( Sum_{k>=1} a(k) * x^k/k ) has integer coefficients and equals (1/x) * Series_Reversion( x / ((1+x)^2 * (1+x^3)) ). See A369443.
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PROG
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(PARI) a(n, s=3, t=1, u=2) = sum(k=0, n\s, binomial(t*n, k)*binomial(u*n, n-s*k));
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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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