login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A000524 Number of rooted trees with n nodes, 2 of which are labeled.
(Formerly M1927 N0761)
12
2, 9, 34, 119, 401, 1316, 4247, 13532, 42712, 133816, 416770, 1291731, 3987444, 12266845, 37627230, 115125955, 351467506, 1070908135, 3257389088, 9892759091, 30002923380, 90879555521, 274963755791, 831064788976 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,1

REFERENCES

J. Riordan, An Introduction to Combinatorial Analysis, Wiley, 1958, p. 134.

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

T. D. Noe, Table of n, a(n) for n=2..200

Index entries for sequences related to rooted trees

Index entries for sequences related to trees

FORMULA

G.f.: A(x) = B(x)^3+2*B(x)^2 where B(x) is g.f. of A000107.

G.f.: A(x) = B(x)^2*(2-B(x))/(1-B(x))^3, where B(x) is g.f. for rooted trees with n nodes, cf. A000081. - Vladeta Jovovic, Oct 19 2001

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-1)^2*(2-B(n-1))/(1-B(n-1))^3, x=0, n+1), x, n): seq(a(n), n=2..25); # 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_] := Coefficient[Series[B[n-1]^2*((2 - B[n-1])/ (1 - B[n-1])^3), {x, 0, n+1}], x, n]; Table[a[n], {n, 2, 25}] (* Jean-Fran├žois Alcover, Dec 20 2012, translated from Alois P. Heinz's Maple program *)

CROSSREFS

Cf. A000081, A000107, A000243, A000269, A000444, A000485, A000525, A000526.

Sequence in context: A301868 A288958 A212348 * A289614 A120989 A280309

Adjacent sequences:  A000521 A000522 A000523 * A000525 A000526 A000527

KEYWORD

nonn,easy,nice

AUTHOR

N. J. A. Sloane

EXTENSIONS

More terms, new description and formula from Christian G. Bower, Nov 15 1999

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified October 19 05:08 EDT 2018. Contains 316336 sequences. (Running on oeis4.)