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A171109
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Gromov-Witten invariants for genus 1.
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4
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0, 0, 1, 225, 87192, 57435240, 60478511040, 96212546526096, 220716443548094400, 702901008498298112640, 3011788599493603375929600, 16916605752011965307094124800, 121848941490162387021464335349760, 1104617766019213143798099163667712000
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OFFSET
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1,4
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LINKS
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MATHEMATICA
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(* b = A013587 *) b[n_] := b[n] = If[n==1, 1, Sum[b[k] b[n-k] k^2 (n-k) (3k-n) (3n-4)!/(3k-1)!/(3(n-k)-2)!, {k, 1, n-1}]];
a[n_] := a[n] = Module[{t1, t2}, t1 = Binomial[n, 3] b[n]; t2 = Sum[ Binomial[3n-1, 3k-1](3k^2-2k)(n-k) b[k] a[n-k], {k, n-1}]; t1/12 + t2/9];
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PROG
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(PARI)
my(a = vector(N), t1, t2); a[1] = 1;
for (n=2, N, a[n] = sum(k=1, n-1,
t1 = binomial(3*n-4, 3*k-2)*(k*(n-k))^2;
t2 = binomial(3*n-4, 3*k-1)*k^3*(n-k);
(t1 - t2)*a[k]*a[n-k])); a;
};
my(a = vector(N), b=A013587_seq(N), t1, t2);
for (n=3, N, t1 = binomial(n, 3)*b[n];
t2 = sum(k=1, n-1, binomial(3*n-1, 3*k-1)*(3*k^2-2*k)*(n-k)*b[k]*a[n-k]);
a[n] = (t1/12 + t2/9)); a;
};
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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