A000529 Powers of rooted tree enumerator. (Formerly M5086 N2202)

20, 74, 186, 388, 721, 1236, 1995, 3072, 4554, 6542, 9152, 12516, 16783, 22120, 28713, 36768, 46512, 58194, 72086, 88484, 107709, 130108, 156055, 185952, 220230, 259350, 303804, 354116, 410843, 474576, 545941, 625600, 714252, 812634, 921522, 1041732, 1174121, 1319588, 1479075, 1653568, 1844098, 2051742, 2277624, 2522916, 2788839, 3076664, 3387713, 3723360, 4085032, 4474210

Offset

1,1

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

Table of n, a(n) for n=1..50.

Simon Plouffe, Approximations de séries génératrices et quelques conjectures, Dissertation, Université du Québec à Montréal, 1992; arXiv:0911.4975 [math.NT], 2009.

Simon Plouffe, 1031 Generating Functions, Appendix to Thesis, Montreal, 1992

Index entries for sequences related to rooted trees

Index entries for sequences related to trees

Maple

A000529:=(z-2)*(3*z**3-12*z**2+18*z-10)/(z-1)**6; [Conjectured by Simon Plouffe in his 1992 dissertation.]
a:= n-> (Matrix([[0, -3, 0, 3, 4, 4]]). Matrix(6, (i, j)-> if (i=j-1) then 1 elif j=1 then [6, -15, 20, -15, 6, -1][i] else 0 fi)^n)[1, 1]: seq(a(n), n=1..24); # Alois P. Heinz, Aug 26 2008

Mathematica

a[n_] := ({0, -3, 0, 3, 4, 4}.MatrixPower[Table[If[i == j-1, 1, If[j == 1, {6, -15, 20, -15, 6, -1}[[i]], 0]], {i, 1, 6}, {j, 1, 6}], n])[[1]]; Table[a[n], {n, 1, 50}] (* Jean-François Alcover, Oct 14 2014, after Alois P. Heinz *)

Crossrefs

Sequence in context: A238026 A010008 A237617 * A238027 A005565 A320484

Adjacent sequences: A000526 A000527 A000528 * A000530 A000531 A000532

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

More terms from Sean A. Irvine, Nov 14 2010

Status

approved