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

0,4

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]

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 *)

Crossrefs

Cf. A135922, A323841, A323842.

Sequence in context: A195192 A103239 A209307 * A132228 A305004 A151879

Adjacent sequences: A323840 A323841 A323842 * A323844 A323845 A323846

Keyword

nonn

Author

N. J. A. Sloane, Feb 04 2019

Extensions

More terms from Alois P. Heinz, Sep 24 2019

Status

approved