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b:= proc(n, i, m) option remember; `if`(n=0, x^m, `if`(i<1, 0, add(g(i)^j*
b(n-i*j, i-1, , max(m, i$j))/j!*multinomialbinomial(n, n-1, i*j, -1), i$j), j=01..n/i)))
a:= n-> (p-> add(coeff(p, x, i)*i, i=1..n))(b(n$2, , 0)):
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Cf. A209324.
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Alois P. Heinz, <a href="/A209327/b209327.txt">Table of n, a(n) for n = 1..385</a>