

A000395


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


5



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
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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

Alois P. Heinz, Table of n, a(n) for n = 6..1000
Index entries for sequences related to rooted trees


FORMULA

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


MAPLE

b:= proc(n) option remember; if n<=1 then n else add(k*b(k)* s(n1, k), k=1..n1)/(n1) fi end: s:= proc(n, k) option remember; add(b(n+1j*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(n5)^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[n1, k], {k, 1, n1}]/(n1)]; s[n_, k_] := s[n, k] = Sum[b[n+1j*k], {j, 1, Quotient[n, k]}]; B[n_] := B[n] = Sum[b[k]*x^k, {k, 1, n}]; a[n_] := SeriesCoefficient[B[n5]^6, {x, 0, n}]; Table[a[n], {n, 6, 30}] (* JeanFrançois Alcover, Oct 13 2014, after Alois P. Heinz *)


CROSSREFS

Cf. A000081, A000106, A000242, A000300, A000343.
Sequence in context: A124641 A169793 A054457 * A005325 A099623 A119852
Adjacent sequences: A000392 A000393 A000394 * A000396 A000397 A000398


KEYWORD

nonn


AUTHOR

N. J. A. Sloane


EXTENSIONS

More terms from Christian G. Bower, Nov 15 1999


STATUS

approved



