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A323843 Number of n-node connected Stanley graphs.

%I A323843 #18 May 24 2020 06:32:36
%S A323843 0,1,1,2,8,52,502,6824,127166,3205924,108975934,5006366048,
%T A323843 312601245662,26708244267148,3142852107059758,512229404374936616,
%U A323843 116165284523764481294,36791597841822774872116,16320947226945992981680606,10163558457757761048966068912
%N A323843 Number of n-node connected Stanley graphs.
%C A323843 For precise definition see Knuth (1997).
%H A323843 Alois P. Heinz, <a href="/A323843/b323843.txt">Table of n, a(n) for n = 0..155</a>
%H A323843 D. E. Knuth, <a href="/A323841/a323841.pdf">Letter to Daniel Ullman and others</a>, Apr 29 1997. [Annotated scanned copy, with permission]
%p A323843 b:= proc(n) option remember; add(mul(
%p A323843       (2^(i+k)-1)/(2^i-1), i=1..n-k), k=0..n)
%p A323843     end:
%p A323843 p:= proc(n) option remember;
%p A323843       add(b(n-j)*binomial(n, j)*(-1)^j, j=0..n)
%p A323843     end:
%p A323843 a:= proc(n) option remember; `if`(n=0, 0, p(n)-add(
%p A323843       binomial(n, j)*p(n-j)*a(j)*j, j=1..n-1)/n)
%p A323843     end:
%p A323843 seq(a(n), n=0..21);  # _Alois P. Heinz_, Sep 24 2019
%t A323843 b[n_] := b[n] = Sum[Product[(2^(i+k) - 1)/(2^i - 1), {i, n-k}], {k, 0, n}];
%t A323843 p[n_] := p[n] = Sum[b[n-j] Binomial[n, j] (-1)^j, {j, 0, n}];
%t A323843 a[n_] := a[n] = If[n == 0, 0, p[n] - Sum[Binomial[n, j] p[n-j] a[j] j, {j, n-1}]/n];
%t A323843 a /@ Range[0, 21] (* _Jean-François Alcover_, May 24 2020, after _Alois P. Heinz_ *)
%Y A323843 Cf. A135922, A323841, A323842.
%K A323843 nonn
%O A323843 0,4
%A A323843 _N. J. A. Sloane_, Feb 04 2019
%E A323843 More terms from _Alois P. Heinz_, Sep 24 2019