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A276018
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n^2 * a(n) = 3*(3*n-2)^2 * a(n-1), with a(0) = 1.
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10
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1, 3, 36, 588, 11025, 223587, 4769856, 105423552, 2391796836, 55365667500, 1302200499600, 31026810250800, 747229013540100, 18158991471060300, 444709995209640000, 10963583748568324800, 271862615765280179025, 6775869970094509098675, 169647707399403264840900, 4264689597367270438867500
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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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n^2 * a(n) = 3*(3*n-2)^2 * a(n-1), with a(0) = 1.
0 = 9*x*(x+27)*y'' + (15*x+243)*y' + y, where y(x) = A(x/-729).
a(n) = 3^(3*n) * Gamma(n+1/3)^2 / (Gamma(1/3)^2 * Gamma(n+1)^2).
a(n) ~ 3^(3*n) / (Gamma(1/3)^2 * n^(4/3)). (End)
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EXAMPLE
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A(x) = 1 + 3*x + 36*x^2 + 588*x^3 + ... is the g.f.
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MATHEMATICA
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Table[FullSimplify[3^(3*n) * Gamma[n + 1/3]^2 / (Gamma[1/3]^2 * Gamma[n+1]^2)], {n, 0, 20}] (* Vaclav Kotesovec, Aug 25 2016 *)
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PROG
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(PARI)
seq(N) = {
a = vector(N); a[1] = 3;
for (n = 2, N, a[n] = 3*(3*n-2)^2/n^2 * a[n-1]);
concat(1, a);
};
seq(20)
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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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