OFFSET
0,3
REFERENCES
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
Gheorghe Coserea, Table of n, a(n) for n = 0..200
L. R. Foulds, R. W. Robinson, Enumeration of binary phylogenetic trees Combinatorial mathematics, VIII (Geelong, 1980), pp. 187-202, Lecture Notes in Math., 884, Springer, Berlin-New York, 1981. Math. Rev. 83a:05071.
L. R. Foulds and R. W. Robinson, Enumeration of binary phylogenetic trees, pp. 187-202, Lecture Notes in Math., 884, Springer, Berlin-New York, 1981. (Annotated scanned copy)
FORMULA
E.g.f: (1 - (1 + 2*exp(x) - 2*exp(x)^2)^(1/2))/exp(x). - Gheorghe Coserea, Aug 04 2015
a(n) = Sum_{j=0..n} C(n,j)*(-1)^(n-j)* Sum_{k=1..j} 2^(1-k)*(2*k-2)!/ (k-1)!* Sum_{i=0..j} stirling2(i,k)*k^(j-i)*C(j,i). - Vladimir Kruchinin, Nov 17 2015
a(n) ~ sqrt(3-sqrt(3)) * n^(n-1) / (log((1+sqrt(3))/2)^(n-1/2) * exp(n)). - Vaclav Kotesovec, Nov 29 2015
MATHEMATICA
CoefficientList[Series[(1 - Sqrt[1 + 2*E^x - 2*E^(2*x)])/E^x, {x, 0, 20}], x] * Range[0, 20]! (* Vaclav Kotesovec, Nov 29 2015 *)
PROG
(PARI) x='x+O('x^33); Vec(serlaplace((1 - (1 + 2*exp(x) - 2*exp(x)^2)^(1/2))/exp(x))) \\ Gheorghe Coserea, Aug 04 2015
(Maxima)
a(n):=sum(((sum((2^(1-k)*(2*k-2)!/(k-1)!*sum((stirling2(i, k)*k^(j-i))*binomial(j, i), i, 0, j)), k, 1, j))*(-1)^(n-j))*binomial(n, j), j, 0, n); /* Vladimir Kruchinin, Nov 17 2015 */
CROSSREFS
KEYWORD
nonn
AUTHOR
EXTENSIONS
More terms from Gheorghe Coserea, Aug 04 2015
STATUS
approved