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A000395 6th power of rooted tree enumerator; number of linear forests of 6 rooted trees.
(Formerly M4175 N1739)
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)



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).


Alois P. Heinz, Table of n, a(n) for n = 6..1000

Index entries for sequences related to rooted trees


G.f.: B(x)^6 where B(x) is g.f. of A000081.


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


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 *)


Cf. A000081, A000106, A000242, A000300, A000343.

Sequence in context: A124641 A169793 A054457 * A005325 A099623 A119852

Adjacent sequences:  A000392 A000393 A000394 * A000396 A000397 A000398




N. J. A. Sloane


More terms from Christian G. Bower, Nov 15 1999



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Last modified December 11 07:30 EST 2019. Contains 329914 sequences. (Running on oeis4.)