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 A225170 Number of non-degenerate fanout-free Boolean functions of n variables having AND rank 1. 3
 2, 4, 32, 416, 7552, 176128, 5018624, 168968192, 6563282944, 288909131776, 14212910809088, 772776684683264, 46017323176296448, 2978458881388183552, 208198894960190160896, 15631251601179130462208 (list; graph; refs; listen; history; text; internal format)
 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. Index entries for sequences related to Boolean functions 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 Cf. A005172. A column of A225171. Sequence in context: A075070 A144937 A009110 * A134958 A101460 A304862 Adjacent sequences: A225167 A225168 A225169 * A225171 A225172 A225173 KEYWORD nonn AUTHOR N. J. A. Sloane, Apr 30 2013 STATUS approved

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Last modified August 3 05:44 EDT 2024. Contains 374875 sequences. (Running on oeis4.)