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A225171 Triangle read by rows: T(n,k), 1 <= k <= n, is the number of non-degenerate fanout-free Boolean functions of n variables having AND rank k. 4
2, 4, 4, 32, 24, 8, 416, 304, 96, 16, 7552, 5440, 1760, 320, 32, 176128, 125824, 41280, 8000, 960, 64, 5018624, 3566080, 1180928, 237440, 31360, 2688, 128, 168968192, 119614464, 39875584, 8212736, 1146880, 111104, 7168, 256 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Also the Bell transform of A225170. For the definition of the Bell transform see A264428. - Peter Luschny, Jan 29 2016

LINKS

Table of n, a(n) for n=1..36.

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.

EXAMPLE

Triangle begins

2,

4,4,

32,24,8,

416,304,96,16,

7552,5440,1760,320,32,

176128,125824,41280,8000,960,64,

5018624,3566080,1180928,237440,31360,2688,128,

168968192,119614464,39875584,8212736,1146880,111104,7168,256,

...

MAPLE

# Function BellMatrix defined in A264428.

BellMatrix(n -> `if`(n=0, 2, add(combinat:-eulerian2(n, k)*2^(2*n-k), k=0..n)), 9); # Peter Luschny, Jan 29 2016

MATHEMATICA

BellMatrix[f_Function, len_] := With[{t = Array[f, len, 0]}, Table[BellY[n, k, t], {n, 0, len - 1}, {k, 0, len - 1}]];

rows = 12;

M = BellMatrix[If[# == 0, 2, Sum[(#+k)!*Sum[(-1)^j/(k-j)!*Sum[(-1)^i*2^(# - i + j)*StirlingS1[# - i + j, j - i]/((# - i + j)!*i!), {i, 0, j}], {j, 1, k}], {k, 1, #}]]&, rows];

Table[M[[n, k]], {n, 2, rows}, {k, 2, n}] // Flatten (* Jean-Fran├žois Alcover, Jun 24 2018, after Peter Luschny *)

CROSSREFS

Columns give A225170 (or A005172), A005756, A224767, A224768.

Sequence in context: A068554 A092524 A137787 * A320600 A290606 A155952

Adjacent sequences:  A225168 A225169 A225170 * A225172 A225173 A225174

KEYWORD

nonn,tabl

AUTHOR

N. J. A. Sloane, Apr 30 2013

STATUS

approved

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Last modified July 2 01:17 EDT 2022. Contains 354984 sequences. (Running on oeis4.)