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A372374
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Coefficient of x^n in the expansion of (1+x+x^3)^(3*n).
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3
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1, 3, 15, 93, 627, 4368, 30957, 222015, 1606803, 11713260, 85884660, 632726988, 4679850525, 34729198260, 258460942671, 1928258130018, 14416834880067, 107993546227875, 810319315565760, 6089298408130707, 45821042464807512, 345217506895648767
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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(3*n,k) * binomial(3*n-k,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+x^3)^3 ). See A372378.
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PROG
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(PARI) a(n, s=3, t=3, u=0) = sum(k=0, n\s, binomial(t*n, k)*binomial((t+u)*n-k, n-s*k));
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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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