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A035049
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E.g.f. satisfies A(x) = x(1+A(A(x))), A(0)=0.
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3
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1, 2, 12, 144, 2760, 74880, 2676240, 120234240, 6571393920, 426547296000, 32283270835200, 2808028566604800, 277433852555059200, 30836115140589158400, 3824551325912308992000, 525674251444773150720000
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OFFSET
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1,2
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LINKS
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Alois P. Heinz, Table of n, a(n) for n = 1..100
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FORMULA
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a(n) = n!*T(n,1), T(n,m) = m/n*sum(k=1..n-m, sum(i=k..n-m, T(n-m,i) * C(i-1,k-1)*(-1)^i)*(-1)^k*C(n+k-1,n-1)), n>m, T(n,n)=1. - Vladimir Kruchinin, May 06 2012
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MAPLE
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A:= proc(n) option remember; local T; if n=0 then 0 else T:= A(n-1); unapply (convert (series (x*(1+T(T(x))), x, n+1), polynom), x) fi end: a:= n-> coeff(A(n)(x), x, n)*n!: seq(a(n), n=1..16); # Alois P. Heinz, Aug 23 2008
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PROG
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(Maxima) T(n, m):=if n=m then 1 else m/n*sum(sum(T(n-m, i)*binomial(i-1, k-1)*(-1)^i, i, k, n-m)*(-1)^k*binomial(n+k-1, n-1), k, 1, n-m); makelist(n!*T(n, 1), n, 1, 10); [Vladimir Kruchinin, May 06 2012]
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CROSSREFS
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Cf. A001028, A030266.
Sequence in context: A067601 A052740 A052742 * A010790 A221101 A187748
Adjacent sequences: A035046 A035047 A035048 * A035050 A035051 A035052
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KEYWORD
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nonn,eigen
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AUTHOR
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Christian G. Bower, Oct 15 1998.
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EXTENSIONS
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More terms from Alois P. Heinz, Aug 23 2008
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STATUS
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approved
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