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A000343
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5th power of rooted tree enumerator; number of linear forests of 5 rooted trees.
(Formerly M3901 N1601)
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6
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1, 5, 20, 70, 230, 721, 2200, 6575, 19385, 56575, 163952, 472645, 1357550, 3888820, 11119325, 31753269, 90603650, 258401245, 736796675, 2100818555, 5990757124, 17087376630, 48753542665, 139155765455, 397356692275, 1135163887190, 3244482184720, 9277856948255
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history;
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OFFSET
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5,2
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REFERENCES
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J. Riordan, An Introduction to Combinatorial Analysis, Wiley, 1958, p. 150.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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Alois P. Heinz, Table of n, a(n) for n = 5..750
Index entries for sequences related to rooted trees
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FORMULA
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G.f.: B(x)^5 where B(x) is g.f. of A000081.
a(n) ~ 5 * A187770 * A051491^n / n^(3/2). - Vaclav Kotesovec, Jan 03 2021
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MAPLE
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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; add(b(k)*x^k, k=1..n) end: a:= n-> coeff(series(B(n-4)^5, x=0, n+1), x, n): seq(a(n), n=5..29); # Alois P. Heinz, Aug 21 2008
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MATHEMATICA
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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] = Sum[b[k]*x^k, {k, 1, n}]; a[n_] := Coefficient[Series[B[n-4]^5, {x, 0, n+1}], x, n]; Table[a[n], {n, 5, 32}] (* Jean-François Alcover, Mar 05 2014, after Alois P. Heinz *)
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CROSSREFS
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Column 5 of A339067.
Cf. A000081, A000106, A000242, A000300, A000395.
Sequence in context: A089094 A080930 A169792 * A005324 A304011 A243869
Adjacent sequences: A000340 A000341 A000342 * A000344 A000345 A000346
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane
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EXTENSIONS
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More terms from Christian G. Bower, Nov 15 1999
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STATUS
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approved
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