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A229285
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G.f.: Sum_{n>=0} x^n / Product_{k=1..2*n-1} (1 - k*x).
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2
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1, 1, 2, 8, 42, 260, 1860, 15020, 134336, 1313696, 13911528, 158279872, 1922455440, 24794405328, 338037825952, 4853075024192, 73123573392416, 1152965052858560, 18974557508679104, 325181733420301504, 5791431588096653824, 106990656473333558528, 2046805540661737323136
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OFFSET
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0,3
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COMMENTS
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Compare to o.g.f. of Bell numbers: Sum_{n>=0} x^n / Product_{k=0..n} (1 - k*x).
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LINKS
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EXAMPLE
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G.f.: A(x) = 1 + x + 2*x^2 + 8*x^3 + 42*x^4 + 260*x^5 + 1860*x^6 +...
where
A(x) = 1 + x/(1-x) + x^2/((1-x)*(1-2*x)*(1-3*x)) + x^3/((1-x)*(1-2*x)*(1-3*x)*(1-4*x)*(1-5*x)) +...
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PROG
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(PARI) {a(n)=local(A=1+x); for(i=1, n, A=1+sum(m=0, n, x^m/prod(k=1, 2*m-1, 1-k*x+x*O(x^n)))); polcoeff(A, n)}
for(n=0, 30, print1(a(n), ", "))
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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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