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A200850
The number of forests of labeled rooted strictly binary trees (each vertex has exactly two children or none) on n nodes.
1
1, 1, 1, 4, 13, 91, 511, 5146, 41329, 544573, 5704381, 93001096, 1203040741, 23391560479, 360416247283, 8142893840446, 145661102170081, 3750604005834361, 76415186203927129, 2209120481052933868, 50510327090854792861, 1620053085929867956291
OFFSET
0,4
LINKS
FORMULA
E.g.f.: exp(A(x)) where A(x) is the e.g.f. for A036770.
Recurrence: 2*a(n) = -(n-2)*(n+1)*a(n-1) + 2*(n-1)*(2*n-3)*a(n-2) + 2*(n-3)*(n-2)*(n-1)^2*a(n-3). - Vaclav Kotesovec, Aug 14 2013
a(n) ~ 2^(n/2+1/2)*n^(n-1)*exp(-n-sqrt(2))*(exp(2*sqrt(2))-(-1)^n). - Vaclav Kotesovec, Aug 14 2013
MAPLE
a:= proc(n) option remember;
`if`(n=0, 1, add((n-1)!/(n-1-2*j)! *binomial(2*j+1, j)/
(2^j) *a(n-1-2*j), j=0..(n-1)/2))
end:
seq(a(n), n=0..30); # Alois P. Heinz, Nov 23 2011
MATHEMATICA
Range[0, 19]! CoefficientList[Series[Exp[(1-(1-2x^2)^(1/2))/x], {x, 0, 19}], x]
CROSSREFS
Cf. A036770.
Sequence in context: A088946 A131590 A281182 * A326565 A041433 A222764
KEYWORD
nonn
AUTHOR
Geoffrey Critzer, Nov 23 2011
STATUS
approved