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A349022
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G.f. satisfies A(x) = 1/(1 - x/(1 - x*A(x))^3)^4.
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1
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1, 4, 22, 152, 1161, 9460, 80550, 708172, 6379368, 58576168, 546215580, 5158542152, 49239812893, 474285453628, 4604149947276, 44999181550032, 442430807369519, 4372944634271688, 43425156714959956, 433049078716727332, 4334925824762251939
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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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If g.f. satisfies: A(x) = 1/(1 - x/(1 - x*A(x))^s)^t, then a(n) = Sum_{k=0..n} binomial(t*n-(t-1)*(k-1),k) * binomial(n+(s-1)*k-1,n-k)/(n-k+1).
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MAPLE
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add(binomial(4*n-3*(k-1), k)*binomial(n+2*k-1, n-k)/(n-k+1), k=0..n) ;
end proc:
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PROG
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(PARI) a(n, s=3, t=4) = sum(k=0, n, binomial(t*n-(t-1)*(k-1), k)*binomial(n+(s-1)*k-1, n-k)/(n-k+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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