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 A006871 Exponentiation of g.f. for rooted trees. 1
 1, 2, 6, 22, 95, 470, 2618, 16159, 109177, 799959, 6309111, 53230208, 477941835, 4546562149, 45646689381, 482052312792, 5338922526947, 61851205026759, 747755335385701, 9413952961001366, 123184994320876476, 1672494478592315483, 23523730530581660635 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Alois P. Heinz, Table of n, a(n) for n = 0..500 MAPLE b:= proc(n) option remember; if n<=1 then n else add(k*b(k)* s(n-1, k), k=1..n-1)/(n-1) fi end: s:= proc(n, k) option remember; add(b(n+1-j*k), j=1..iquo(n, k)) end: B:= proc(n) option remember; unapply(add(b(k)*x^k/k!, k=1..n), x) end: a:= n-> coeff(series(exp(B(n+1)(x)), x=0, n+2), x, n+1)*(n+1)!: seq(a(n), n=0..20); # Alois P. Heinz, Aug 22 2008 # second Maple program: with(numtheory): g:= proc(n) option remember; `if`(n<=1, n, (add(add(d*       g(d), d=divisors(j))*g(n-j), j=1..n-1))/(n-1))     end: b:= proc(n) option remember; `if`(n=0, 1, add(       binomial(n-1, j-1)*g(j)*b(n-j), j=1..n))     end: a:= n-> b(n+1): seq(a(n), n=0..30);  # Alois P. Heinz, Mar 18 2015 MATHEMATICA b[n_] := b[n] = If[n <= 1, n, Sum[k*b[k]*s[n-1, k], {k, 1, n-1}]/(n-1)]; s[n_, k_] := s[n, k] = Sum[b[n+1-j*k], {j, 1, Quotient[n, k]}]; B[n_] := B[n] = Function[x, Evaluate @ Sum[b[k]*x^k/k!, {k, 1, n}]]; a[n_] := Coefficient[Series[Exp[B[n+1][x]], {x, 0, n+2}], x, n+1]*(n+1)!; Table[a[n], {n, 0, 30}] (* Jean-François Alcover, Feb 17 2014, after Alois P. Heinz *) CROSSREFS Cf. A000081. Sequence in context: A093793 A087959 A292096 * A268699 A253948 A248836 Adjacent sequences:  A006868 A006869 A006870 * A006872 A006873 A006874 KEYWORD nonn AUTHOR STATUS approved

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Last modified August 16 05:55 EDT 2022. Contains 356160 sequences. (Running on oeis4.)