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A275763
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G.f.: x = Sum_{n>=1} a(n-1) * x^n / Product_{k=1..n} (1 + n*k*x).
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0
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1, 1, 5, 63, 1514, 59685, 3512620, 289374295, 31846112564, 4518890895645, 804124456255680, 175478742025495755, 46106223230016643056, 14363471037818609599893, 5236804141734580288633760, 2209636417728549950873988255, 1068573377399399933312154968064, 587247047578198565707709826415149, 364003505996839798561347571968317760, 252786592402514515785220127177096089395
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OFFSET
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0,3
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COMMENTS
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Compare g.f. to:
(1) x = Sum_{n>=1} (n-1)! * x^n / Product_{k=1..n} (1 + k*x).
(2) x = Sum_{n>=1} n^(n-2) * x^n / (1 + n*x)^n.
(3) x = Sum_{n>=1} (n-1)!^2 * x^n / Product_{k=1..n} (1 + k^2*x).
(4) x = Sum_{n>=1} A082157(n-1) * x^n / (1 + n^2*x)^n.
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LINKS
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EXAMPLE
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G.f.: x = 1*x/(1+x) + 1*x^2/((1+2*1*x)*(1+2*2*x)) + 5*x^3/((1+3*1*x)*(1+3*2*x)*(1+3*3*x)) + 63*x^4/((1+4*1*x)*(1+4*2*x)*(1+4*3*x)*(1+4*4*x)) + 1514*x^5/((1+5*1*x)*(1+5*2*x)*(1+5*3*x)*(1+5*4*x)*(1+5*5*x)) + 59685*x^6/((1+6*1*x)*(1+6*2*x)*(1+6*3*x)*(1+6*4*x)*(1+6*5*x)*(1+6*6*x)) +...
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PROG
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(PARI) {a(n) = my(A=[1]); for(i=1, n, A = concat(A, 0); A[#A] = -Vec(sum(m=1, #A, A[m]*x^m/prod(k=1, m, (1 + m*k*x +x*O(x^#A) ) ) ) )[#A] ); A[n+1]}
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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