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

 

Logo

Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing.
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A108643 Number of binary rooted trees with n nodes and internal path length n. 6
1, 1, 0, 2, 0, 1, 4, 0, 4, 2, 8, 6, 8, 8, 8, 40, 4, 29, 40, 52, 56, 64, 116, 112, 200, 86, 296, 366, 360, 432, 652, 800, 840, 1470, 1116, 2048, 2356, 3052, 3524, 4220, 5648, 6964, 9660, 8688, 14128, 17024, 19432, 23972, 32784, 37873, 44912, 59672, 67560, 93684 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

Self-convolution equals A095830 (number of binary trees of path length n). - Paul D. Hanna, Aug 20 2007

REFERENCES

Knuth Vol. 1 Sec. 2.3.4.5, Problem 5.

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..1000

FORMULA

G.f. = B(w, w) where B(w, z) is defined in A095830.

G.f.: A(x) = 1 + x*(A_2)^2; A_2 = 1 + x^2*(A_3)^2; A_3 = 1 + x^3*(A_4)^2; ... A_n = 1 + x^n*(A_{n+1})^2 for n>=1 with A_1 = A(x). - Paul D. Hanna, Aug 20 2007

MAPLE

A:= proc(n, k) option remember; if n=0 then 1 else convert(series(1+ x^k*A(n-1, k+1)^2, x, n+1), polynom) fi end: a:= n-> coeff(A(n, 1), x, n): seq(a(n), n=0..60);  # Alois P. Heinz, Aug 22 2008

MATHEMATICA

A[n_, k_] := A[n, k] = If[n==0, 1, 1+x^k*A[n-1, k+1]^2 + O[x]^(n+1) // Normal]; a[n_] := SeriesCoefficient[A[n, 1], {x, 0, n}]; Table[a[n], {n, 0, 60}] (* Jean-Fran├žois Alcover, Mar 14 2017, after Alois P. Heinz *)

PROG

(PARI) {a(n)=local(A=1+x*O(x^n)); for(j=0, n-1, A=1+x^(n-j)*A^2); polcoeff(A, n)} - Paul D. Hanna, Aug 20 2007

CROSSREFS

Sequence in context: A039991 A081265 A273821 * A133838 A182138 A258123

Adjacent sequences:  A108640 A108641 A108642 * A108644 A108645 A108646

KEYWORD

nonn

AUTHOR

N. J. A. Sloane and Nadia Heninger, Jul 08 2005

EXTENSIONS

More terms from Vladeta Jovovic, Jul 08 2005

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
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 5 17:42 EST 2019. Contains 329768 sequences. (Running on oeis4.)