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-François 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
KEYWORD
nonn
AUTHOR
N. J. A. Sloane and Nadia Heninger, Jul 08 2005
EXTENSIONS
More terms from Vladeta Jovovic, Jul 08 2005
STATUS
approved