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

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.

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.

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