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A002857 Number of Post functions of n variables.
(Formerly M3078 N1249)
5
1, 3, 20, 996, 9333312, 6406603084568576, 16879085743296493582043922521915392, 717956902513121252476003434439730211917452457474409186632352788205535232 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

REFERENCES

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Wheeler, Roger F.; Complete propositional connectives. Z. Math. Logik Grundlagen Math. 7 1961 185-198.

LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..12

R. F. Wheeler, Complete propositional connectives, Z. Math. Logik Grundlagen Math. 7 1961 185-198. [Annotated scanned copy]

R. F. Wheeler, An asymptotic formula for the number of complete propositional connectives, Z. Math. Logik Grundlagen Math. 8 (1962), 1-4. [Annotated scanned copy]

MAPLE

b:= proc(n, i, l) `if`(n=0, 2^(w-> add(mul(2^igcd(t, l[h]),

      h=1..nops(l)), t=1..w)/w)(ilcm(l[])), `if`(i<1, 0,

      add(b(n-i*j, i-1, [l[], i$j])/j!/i^j, j=0..n/i)))

    end:

a:= n-> b(n$2, [])/4:

seq(a(n), n=1..8);  # Alois P. Heinz, Aug 14 2019

MATHEMATICA

b[n_, i_, l_] := If[n==0, 2^Function[w, Sum[Product[2^GCD[t, l[[h]]], {h, 1, Length[l]}], {t, 1, w}]/w][LCM @@ l], If[i < 1, 0, Sum[b[n - i j, i-1, Join[l, Table[i, {j}]]]/j!/i^j, {j, 0, n/i}]]];

a[n_] := b[n, n, {}]/4;

Array[a, 8] (* Jean-Fran├žois Alcover, Oct 27 2020, after Alois P. Heinz *)

CROSSREFS

Equals A000612/2 and A003180/4.

Sequence in context: A108699 A162134 A296408 * A203314 A174652 A024011

Adjacent sequences:  A002854 A002855 A002856 * A002858 A002859 A002860

KEYWORD

nonn

AUTHOR

N. J. A. Sloane.

EXTENSIONS

More terms from Vladeta Jovovic, Feb 23 2000

STATUS

approved

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Last modified May 16 13:40 EDT 2021. Contains 343947 sequences. (Running on oeis4.)