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A370280
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Coefficient of x^n in the expansion of 1/( (1-x)^2 - x )^n.
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1
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1, 3, 25, 234, 2305, 23373, 241486, 2527920, 26720529, 284555700, 3048323135, 32812937820, 354619072990, 3845377105794, 41817926091120, 455893204069944, 4980851709418353, 54521955043418925, 597823622561048020, 6564929893462467450, 72189820135528858455
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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..n} binomial(n+k-1,k) * binomial(3*n+k-1,n-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 - x) ).
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PROG
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(PARI) a(n) = sum(k=0, n, binomial(n+k-1, k)*binomial(3*n+k-1, n-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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