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A370626
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Coefficient of x^n in the expansion of 1 / (1-x-x^3)^(2*n).
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0
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1, 2, 10, 62, 402, 2662, 17914, 122040, 839154, 5811758, 40482530, 283311470, 1990464450, 14030571258, 99179197512, 702789627712, 4990636603986, 35506061422530, 253030893941362, 1805893735209486, 12906043894108162, 92346511605008562, 661494201448139850
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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(2*n+k-1,k) * binomial(3*n-2*k-1,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)^2 ). See A368962.
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PROG
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(PARI) a(n, s=3, t=2, u=0) = sum(k=0, n\s, binomial(t*n+k-1, k)*binomial((t-u+1)*n-(s-1)*k-1, 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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