A323843 Number of n-node connected Stanley graphs.

0, 1, 1, 2, 8, 52, 502, 6824, 127166, 3205924, 108975934, 5006366048, 312601245662, 26708244267148, 3142852107059758, 512229404374936616, 116165284523764481294, 36791597841822774872116, 16320947226945992981680606, 10163558457757761048966068912

Offset: 0

Author

N. J. A. Sloane, Feb 04 2019

Keywords

• nonn

Comments

For precise definition see Knuth (1997).

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..155
• D. E. Knuth, Letter to Daniel Ullman and others, Apr 29 1997. [Annotated scanned copy, with permission]

Crossrefs

Cf. A135922, A323841, A323842.

Programs

Maple

b:= proc(n) option remember; add(mul(
      (2^(i+k)-1)/(2^i-1), i=1..n-k), k=0..n)
    end:
p:= proc(n) option remember;
      add(b(n-j)*binomial(n, j)*(-1)^j, j=0..n)
    end:
a:= proc(n) option remember; `if`(n=0, 0, p(n)-add(
      binomial(n, j)*p(n-j)*a(j)*j, j=1..n-1)/n)
    end:
seq(a(n), n=0..21);  # Alois P. Heinz, Sep 24 2019

Mathematica

b[n_] := b[n] = Sum[Product[(2^(i+k) - 1)/(2^i - 1), {i, n-k}], {k, 0, n}];
p[n_] := p[n] = Sum[b[n-j] Binomial[n, j] (-1)^j, {j, 0, n}];
a[n_] := a[n] = If[n == 0, 0, p[n] - Sum[Binomial[n, j] p[n-j] a[j] j, {j, n-1}]/n];
a /@ Range[0, 21] (* Jean-François Alcover, May 24 2020, after Alois P. Heinz *)

Extensions

More terms from Alois P. Heinz, Sep 24 2019