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A323843 Number of n-node connected Stanley graphs. 5
0, 1, 1, 2, 8, 52, 502, 6824, 127166, 3205924, 108975934, 5006366048, 312601245662, 26708244267148, 3142852107059758, 512229404374936616, 116165284523764481294, 36791597841822774872116, 16320947226945992981680606, 10163558457757761048966068912 (list; graph; refs; listen; history; text; internal format)
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-Fran├žois 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

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Last modified August 4 07:49 EDT 2021. Contains 346445 sequences. (Running on oeis4.)