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A000395 6th power of rooted tree enumerator; number of linear forests of 6 rooted trees.
(Formerly M4175 N1739)
6
1, 6, 27, 104, 369, 1236, 3989, 12522, 38535, 116808, 350064, 1039896, 3068145, 9004182, 26314773, 76652582, 222705603, 645731148, 1869303857, 5404655358, 15611296146, 45060069406, 129989169909, 374843799786, 1080624405287 (list; graph; refs; listen; history; text; internal format)
OFFSET
6,2
REFERENCES
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).
LINKS
FORMULA
G.f.: B(x)^6 where B(x) is g.f. of A000081.
a(n) ~ 6 * A187770 * A051491^n / n^(3/2). - Vaclav Kotesovec, Jan 03 2021
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; add(b(k)*x^k, k=1..n) end: a:= n-> coeff(series(B(n-5)^6, x=0, n+1), x, n): seq(a(n), n=6..30); # Alois P. Heinz, Aug 21 2008
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] = Sum[b[k]*x^k, {k, 1, n}]; a[n_] := SeriesCoefficient[B[n-5]^6, {x, 0, n}]; Table[a[n], {n, 6, 30}] (* Jean-François Alcover, Oct 13 2014, after Alois P. Heinz *)
CROSSREFS
Column 6 of A339067.
Sequence in context: A124641 A169793 A054457 * A005325 A099623 A119852
KEYWORD
nonn
AUTHOR
EXTENSIONS
More terms from Christian G. Bower, Nov 15 1999
STATUS
approved

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Last modified April 18 18:58 EDT 2024. Contains 371781 sequences. (Running on oeis4.)