OFFSET
1,1
COMMENTS
Apart from initial term, same as A005172, which is the main entry for this sequence.
LINKS
Vaclav Kotesovec, Table of n, a(n) for n = 1..241
J. P. Hayes, Enumeration of fanout-free Boolean functions, J. ACM, 23 (1976), 700-709.
FORMULA
Hayes (1976, Theorem 3) gives a recurrence.
G.f.: 1/Q(0) + 1, where Q(k)= 1 - 2*x*(k+1) - 2*x*(k+1)/Q(k+1); (continued fraction). - Sergei N. Gladkovskii, May 18 2013
a(n) ~ (log(2)-1/2)^(1/2 - n) * n^(n-1) / exp(n). - Vaclav Kotesovec, Oct 19 2016
MATHEMATICA
max = 16; s = -ProductLog[-Exp[x-1/2]/2] + O[x]^max; Join[{2}, Drop[CoefficientList[s, x]*Range[0, max-1]!, 2]] (* Jean-François Alcover, Oct 18 2016 *)
a[1] = 2; a[n_] := (Sum[(n + k - 1)!*Sum[(-1)^j/(k - j)!*Sum[(-1)^i*2^(n - i + j - 1)*StirlingS1[n - i + j - 1, j - i]/((n - i + j - 1)!*i!), {i, 0, j}], {j, 1, k}], {k, 1, n - 1}]);
Array[a, 20] (* Jean-François Alcover, Jun 24 2018, after Vladimir Kruchinin *)
CROSSREFS
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Apr 30 2013
STATUS
approved