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A364336
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G.f. satisfies A(x) = (1 + x) * (1 + x*A(x)^3).
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12
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1, 2, 7, 39, 242, 1634, 11631, 85957, 653245, 5072862, 40077807, 321106623, 2602911282, 21308131235, 175909559897, 1462846379247, 12242600576066, 103035285071630, 871490142773640, 7404121610615520, 63157400073057627, 540689217572662413, 4644083121177225292
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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(3*k+1,k) * binomial(3*k+1,n-k) / (3*k+1).
D-finite with recurrence -2*n*(2*n+1)*a(n) +(3*n^2+23*n-14)*a(n-1) +(207*n^2 -635*n +494)*a(n-2) +2*(397*n^2 -2031*n +2600)*a(n-3) +6*(75*n-244) *(3*n-11)*a(n-4) +9*(45*n-179) *(3*n-14)*a(n-5) +63*(3*n-14) *(3*n-17)*a(n-6) +12*(3*n-16) *(3*n-20)*a(n-7)=0. - R. J. Mathar, Jul 25 2023
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MAPLE
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add( binomial(3*k+1, k) * binomial(3*k+1, n-k)/(3*k+1), k=0..n) ;
end proc:
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MATHEMATICA
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nmax = 80; A[_] = 1;
Do[A[x_] = (1 + x)*(1 + x*A[x]^3) + O[x]^(nmax+1) // Normal, {nmax+1}];
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PROG
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(PARI) a(n) = sum(k=0, n, binomial(3*k+1, k)*binomial(3*k+1, n-k)/(3*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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